How to do this

-4x^2+12x-2=p(x)*(2x-1)+3

$\begin{array}{|rcll|} \hline p(x)*(2x-1)+3&=& -4x^2+12x-2 \quad &| \quad - 3 \\ p(x) &=& -4x^2+12x-5 \quad &| \quad :(2x-1)\\ p(x) &=& \frac{-4x^2+12x-5}{2x-1} \\ && -4x^2+12x-5 : 2x-1 = -2x+5 \\ p(x) &=& -2x+5 \\ \hline \end{array}$

Check:

$\begin{array}{|rcll|} \hline && (-2x+5)\cdot (2x-1)+3 \\ &=& -4x^2+2x+10x-5+3 \\ &=& -4x^2+12x-2\ \checkmark \\ \hline \end{array}$