Answer
$2(x-2)(3x+1)$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
6x^2-10x-4
\\\\=
2(3x^2-5x-2)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2(3x^2-5x-2)
\end{array} has $ac=
3(-2)=-6
$ and $b=
-5
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-6,1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2(3x^2-6x+1x-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[(3x^2-6x)+(x-2)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2[3x(x-2)+(x-2)]
.\end{array}
Factoring the $GCF=
(x-2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
2[(x-2)(3x+1)]
\\\\=
2(x-2)(3x+1)
.\end{array}