Answer
$-2(4a-3b)(3a-2b)$
Work Step by Step
Factoring the negative $GCF=
-2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-24a^2+34ab-12b^2
\\\\=
-2(12a^2-17ab+6b^2)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-2(12a^2-17ab+6b^2)
\end{array} has $ac=
12(6)=72
$ and $b=
-17
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,-8
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-2(12a^2-9ab-8ab+6b^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}
-2[(12a^2-9ab)-(8ab-6b^2)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-2[3a(4a-3b)-2b(4a-3b)]
.\end{array}
Factoring the $GCF=
(4a-3b)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-2[(4a-3b)(3a-2b)]
\\\\=
-2(4a-3b)(3a-2b)
.\end{array}