Ttdfjt

documentclass[a4paper, 12pt]article
usepackageamsfonts
%usepackageamsbsy
usepackageamssymb
usepackageamsmath

begindocument
beginmultline*
Psi(Gamma_k,x)= x,(x-1)^(6k-2),left(x^3-(3k+5)x^2+(2k^2+8k+7)x-(3+3k)right)left(x^2-(k+3)x+2right)\,left(x^2-(2k+4)x+1right)
endmultline*
enddocument

I am trying to write this mathematical equation in Latex. But how to break such kind of equation such that it lies in the paragraph itself. In my case, it comes out of the margin in the page.

Why not use a simple align*?

documentclass[a4paper, 12pt]article
usepackageamsfonts
%usepackageamsbsy
usepackageamssymb
usepackageamsmath
usepackageshowframe
renewcommandShowFrameLinethickness0.3pt

begindocument

beginalign*
Psi(Gamma_k,x) =x(x-1)^(6k-2) & timesbigl(x^3-(3k+5) x^2+(2k^2+8k+7)x-(3+3k) bigr) \ & times bigl(x^2-(k+3)x+2bigr)bigl(x^2-(2k+4)x+1 bigr)
endalign*

enddocument 

documentclass[a4paper, 12pt]article
usepackageamsmath

begindocument
 beginmultline*
 Psi(Gamma_k,x)= x,(x-1)^(6k-2)\
 cdotleft(x^3-(3k+5)x^2+(2k^2+8k+7)x-(3+3k)right)\
 cdotleft(x^2-(k+3)x+2right)cdotleft(x^2-(2k+4)x+1right)
 endmultline*
enddocument

I'm not a fan of multline so here is my take using MoveEqLeft from mathtools

The look is similar to Sebastianos answer, but does not use alignment on =

documentclass[a4paper, 12pt]article
%usepackageamsfonts % already loaded through amssymb
%usepackageamsbsy
usepackageamssymb
usepackageamsmath
usepackagemathtools
begindocument
beginalign*
 MoveEqLeft Psi(Gamma_k,x)= x(x-1)^(6k-2)
 \
 &timesbigl(x^3-(3k+5)x^2+(2k^2+8k+7)x-(3+3k)bigr)
 \
 &timesbigl(x^2-(k+3)x+2bigr)bigl(x^2-(2k+4)x+1bigr)
endalign*
enddocument

This is the type of alignment (when I'm not aligning on relations) that I use all the time in my edits. It comes from https://www.ams.org/publications/authors/mit-2.pdf, see section 3.3.4

If you want to break your formula into several lines in column, you can use the split environment. See this little example (first edit) with the very good suggestion of @Bernard user (see the first comment).

documentclass[a4paper,12pt]article
usepackageamsmath,amssymb

begindocument
beginequation*
 beginsplit
Psi(Gamma_k,x) & = x(x-1)^(6k-2)\
& phantom=cdot left(x^3-(3k+5)x^2+(2k^2+8k+7)x-(3+3k)right)left(x^2-(k+3)x+2right)\
& phantom=cdot left(x^2-(2k+4)x+1right)
 endsplit
endequation*
enddocument

EDIT 2: Here I have approved the suggestion of the very good user @dailef (see your comment).

documentclass[a4paper,12pt]article
usepackageamsmath,amssymb
begindocument
beginequation*
 beginsplit
Psi(Gamma_k,x) = & x(x-1)^(6k-2)\
& cdot left(x^3-(3k+5)x^2+(2k^2+8k+7)x-(3+3k)right)left(x^2-(k+3)x+2right)\
& cdot left(x^2-(2k+4)x+1right)
 endsplit
endequation*
enddocument