Answer
$4(x+6)(3x-1)$
Work Step by Step
Factoring the $GCF=
4
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
12x^2+68x-24
\\\\=
4(3x^2+17x-6)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
4(3x^2+17x-6)
\end{array} has $ac=
3(-6)=-18
$ and $b=
17
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
18,-1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
4(3x^2+18x-1x-6)
.\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}
4[(3x^2+18x)-(x+6)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
4[3x(x+6)-(x+6)]
.\end{array}
Factoring the $GCF=
(x+6)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
4[(x+6)(3x-1)]
\\\\=
4(x+6)(3x-1)
.\end{array}
