Cfxtrjtrk

I would use something like this

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}

begin{document}

Blah blah

[f(z)=frac{1}{382112640}cdotfrac{A}{B}]

where

begin{align*}

    A=&,-306772802511648469920eta^4z^4+762453974480763801600eta^5z^4\

    &,-1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3\

    &,+11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2\

    &,-78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2\

    &,+228927087397104405937944eta^3z^2+999881065017543109136462eta^3z\

    &,-317254092617698017425280eta^5z-443761561344388063474665eta^4z\

    &,+82327155732241730770824eta z-514623285385260545505123eta^2z\

    &,-1010535343560043404912120eta^2-357788302700438191196160eta^5\

    &,-43808044579418934376632-214023244873618345872240eta^4\

    &,+11818373349781028079eta^3+347370177721463765064153eta

end{align*}

and

[B=(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)]

end{document}

I suggest something line the following, so the wide terms are reduced.

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}



begin{document}



begin{gather*}

begin{align*}

g(eta,z)&=

parbox[t]{0.85displaywidth}{raggedright

$-306772802511648469920eta^4z^4+

762453974480763801600eta^5z^4-

1678626210368271790080eta^5z^3-

28510918043555533736160eta^4z^3+

11443138641451067779872eta^3z^3-

52164076923190540413504eta^2z^2-

78145258181161076156160eta^5z^2-

211306163712129371808450eta^4z^2+

228927087397104405937944eta^3z^2+

999881065017543109136462eta^3z-

317254092617698017425280eta^5z-

443761561344388063474665eta^4z+

82327155732241730770824eta z-

514623285385260545505123eta^2z-

1010535343560043404912120eta^2-

357788302700438191196160eta^5-

43808044579418934376632-

214023244873618345872240eta^4+

11818373349781028079eta^3+

347370177721463765064153eta$

}

\[2ex]

h(z)&=(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)

end{align*}

\[2ex]

f(z)=frac{1}{382112640}frac{g(eta,z)}{h(z)}

end{gather*}



end{document}

or

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools, nccmath}

begin{document}

    begin{multline*}medmath

f(z)=frac{1}{382112640}

    frac{left[

    begin{multlined}

    -306772802511648469920eta^4z^4+762453974480763801600eta^5z^4-\

    1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3+\

    11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2-\

    78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2+\

    228927087397104405937944eta^3z^2+999881065017543109136462eta^3z-\

    317254092617698017425280eta^5z-443761561344388063474665eta^4z+\

    82327155732241730770824eta z - 514623285385260545505123eta^2z-\

    1010535343560043404912120eta^2-357788302700438191196160eta^5-\

    43808044579418934376632-214023244873618345872240eta^4+\

    11818373349781028079eta^3+347370177721463765064153eta

    end{multlined}right]}

    {(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)}

    end{multline*}

Given the nature of the operations, you can probably express this in a tidy manner using matrix multiplication notation, eg:

where:

Code:

$$ f(z)=frac{1}{382,112,640} ; frac{g(eta, z)}{u(z) , v(z) , w(z) } $$



where



$$

begin{array}{ll}

  g(eta, z) = 

  begin{bmatrix} 

    begin{array}{r @{hspace{0em}} r}

      - & 306,772,802,511,648,469,920 \

        & 762,453,974,480,763,801,600 \

      - & 1,678,626,210,368,271,790,080 \

      - & 28,510,918,043,555,533,736,160 \

       & 11,443,138,641,451,067,779,872 \

      - & 52,164,076,923,190,540,413,504 \

      - & 78,145,258,181,161,076,156,160 \

      - & 211,306,163,712,129,371,808,450 \

       & 228,927,087,397,104,405,937,944 \

       & 999,881,065,017,543,109,136,462 \

      - & 317,254,092,617,698,017,425,280 \

      - & 443,761,561,344,388,063,474,665 \

       & 82,327,155,732,241,730,770,824 \

      - & 514,623,285,385,260,545,505,123 \

      - & 1,010,535,343,560,043,404,912,120 \

      - & 357,788,302,700,438,191,196,160 \

      - & 43,808,044,579,418,934,376,632 \

      - & 214,023,244,873,618,345,872,240 \

       & 11,818,373,349,781,028,079 \

       & 347,370,177,721,463,765,064,153

    end{array}

  end{bmatrix}^T

  begin{bmatrix}

    begin{array}{l}

      eta^4z^4 \

      eta^5z^4 \

      eta^5z^3 \

      eta^4z^3 \

      eta^3z^3 \

      eta^2z^2 \

      eta^5z^2 \

      eta^4z^2 \

      eta^3z^2 \

      eta^3z \

      eta^5z \

      eta^4z \

      eta z \

      eta^2z \

      eta^2 \

      eta^5 \

      1 \

      eta^4 \

      eta^3 \

      eta

    end{array}

  end{bmatrix}

  & 

  begin{array}{l}

    u(z) = begin{bmatrix} begin{array}{r @{hspace{0em}} r} & 417,420 \ - & 4,169,121 \ - & 15,571,312 end{array}end{bmatrix}^T begin{bmatrix} begin{array}{l} z^2 \ z \ 1 end{array}end{bmatrix}\[3em]

    v(z) = begin{bmatrix} begin{array}{r @{hspace{0em}} r}  & 1,546 \ & 3,537 end{array}end{bmatrix}^T begin{bmatrix}begin{array}{l} z \ 1 end{array}end{bmatrix}\[3em]

    w(z) = begin{bmatrix}begin{array}{r @{hspace{0em}} r}  & 3,092 \ & 17,001 end{array}end{bmatrix}^T begin{bmatrix}begin{array}{l} z \ 1 end{array}end{bmatrix} \[3em]

  end{array}

end{array}

$$

PS. Having said that, given the nature of the numbers involved, I would also agree with Mefitico's point of view in the comments, i.e. it's best to create a variable with indices and express via a cleaner expression, and then refer to a table mapping those indices to the actual numbers involved.

I recommend aligning the variables and adding some form of thousand-separators, both will enhance the readability. What I also recommend (but didn't do here) is sorting by the powers of the first and then the second variable. This is a modification of JuleV's answer.

documentclass{article}

%usepackage{amsmath}% Loaded by mathtools

usepackage{mathtools}

begin{document}

Blah blah

[f(z)=frac{1}{382112640}cdotfrac{A}{B}]

where

[

arraycolsep=0.5pt

begin{array}{rrllrll}

    A=&,      -306,772,802,511,648,469,920 &eta^4 &z^4 &      +762,453,974,480,763,801,600 &eta^5 &z^4\

    &,     -1,678,626,210,368,271,790,080 &eta^5 &z^3 &  -2,8510,918,043,555,533,736,160 &eta^4 &z^3\

    &,    +11,443,138,641,451,067,779,872 &eta^3 &z^3 &  -5,2164,076,923,190,540,413,504 &eta^2 &z^2\

    &,    -78,145,258,181,161,076,156,160 &eta^5 &z^2 & -21,1306,163,712,129,371,808,450 &eta^4 &z^2\

    &,   +228,927,087,397,104,405,937,944 &eta^3 &z^2 & +99,9881,065,017,543,109,136,462 &eta^3 &z\

    &,   -317,254,092,617,698,017,425,280 &eta^5 &z   & -44,3761,561,344,388,063,474,665 &eta^4 &z\

    &,    +82,327,155,732,241,730,770,824 &eta   &z   & -51,4623,285,385,260,545,505,123 &eta^2 &z\

    &,-1,010,535,343,560,043,404,912,120 &eta^2 &    & -35,7788,302,700,438,191,196,160 &eta^5 &\

    &,    -43,808,044,579,418,934,376,632 &       &    & -21,4023,244,873,618,345,872,240 &eta^4 &\

    &,         +11,818,373,349,781,028,079 &eta^3 &    & +34,7370,177,721,463,765,064,153 &eta   &

end{array}

]

and

[B=(417,420z^2-4,169,121z-15,571,312)(1,546z+3,537)(3,092z+17,001)]

end{document}

I'm sure there are also some custom packages that can do this for you but this is just using the packages you provided:

I would usually use the package breqn. That automatically line-breaks equations, and has a lot of very nice features, but uses low-level having into the maths primitives, which means it tends to make a mess of other packages what do the same thing (for example, you can't use both breqn and sansmath in the same document)

begin{dmath*}

f(z)=frac{1}{382112640}times-306772802511648469920eta^4z^4+left(762453974480763801600eta^5z^4-1678626210368271790080eta^5z^3-28510918043555533736160eta^4z^3+11443138641451067779872eta^3z^3-52164076923190540413504eta^2z^2-78145258181161076156160eta^5z^2-211306163712129371808450eta^4z^2+228927087397104405937944eta^3z^2+999881065017543109136462eta^3z-317254092617698017425280eta^5z-443761561344388063474665eta^4z+82327155732241730770824eta z-514623285385260545505123eta^2z-1010535343560043404912120eta^2-357788302700438191196160eta^5-43808044579418934376632-214023244873618345872240eta^4+11818373349781028079eta^3+347370177721463765064153etaright)timesleft(left(417420z^2-4169121z-15571312right)left(1546z+3537right)left(3092z+17001right)right)^{-1}

end{dmath*}

which produces

IMO the right-alignment is ugly but apparently that's the AMS standard - without the brackets it left aligns all those lines like the alginat version.

Following the original disposition of the function, but using alignat, parenthesis, and fractions to emphasize its different terms.

documentclass{article}



usepackage{mathtools}



begin{document}



begin{alignat*}{2}

& f(z) && = frac{1}{382112640} times left( vphantom{frac{1}{382112640}} -306772802511648469920 eta^4 z^4 + 762453974480763801600 eta^5 z^4 right. \[1.5ex] 

& && -1678626210368271790080 eta^5 z^3 -28510918043555533736160 eta^4 z^3 \[1.5ex]

& && +11443138641451067779872 eta^3 z^3 -52164076923190540413504 eta^2 z^2 \[1.5ex]

& && -78145258181161076156160 eta^5 z^2 -211306163712129371808450 eta^4 z^2 \[1.5ex]

& && +228927087397104405937944 eta^3 z^2 +999881065017543109136462 eta^3 z \[1.5ex]

& && -317254092617698017425280 eta^5 z -443761561344388063474665 eta^4 z \[1.5ex]

& && +82327155732241730770824 eta z -514623285385260545505123 eta^2 z \[1.5ex]

& && -1010535343560043404912120 eta^2 -357788302700438191196160 eta^5 \[1.5ex]

& && -43808044579418934376632 -214023244873618345872240 eta^4 \[1.5ex]

& && +11818373349781028079 eta^3 +347370177721463765064153eta left. vphantom{frac{1}{382112640}} right) \[1.5ex]

& && times frac{1}{(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)}

end{alignat*}



end{document}