$\dfrac{dy}{dx}=\dfrac{3x^2+4x+2}{2(y-1)}$
$2(y-1)dy=(3x^2+4x+2)dx$
you should be able to finish it from here.
So y^2 -2y = x^3+2x^2+2x+C
what should i do with y^2-2y(2 y variable) that is the question ?
I'm newbie with dif equ i don't have any experience with problem
i just learn a easy seperation problem
ex dy/dx = y that y has only one variable on the left side