Answer
$-(4-3x)(5-4x)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-20+31x-12x^2
\end{array} has $ac=
-20(-12)=240
$ and $b=
31
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
15,16
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-20+15x+16x-12x^2
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(-20+15x)+(16x-12x^2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-5(4-3x)+4x(4-3x)
.\end{array}
Factoring the $GCF=
(4-3x)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(4-3x)(-5+4x)
\\\\=
-(4-3x)(5-4x)
.\end{array}