Answer
$(2-3x)(5-4x)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
10-23x+12x^2
\end{array} has $ac=
10(12)=120
$ and $b=
-23
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-15,-8
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
10-15x-8x+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}
(10-15x)-(8x-12x^2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5(2-3x)-4x(2-3x)
.\end{array}
Factoring the $GCF=
(2-3x)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2-3x)(5-4x)
.\end{array}
