Answer
$2x(3x-5)(x+1)$
Work Step by Step
Factoring the $GCF=
2x
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
6x^3-4x^2-10x
\\\\=
2x(3x^2-2x-5)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2x(3x^2-2x-5)
\end{array} has $ac=
3(-5)=-15
$ and $b=
-2
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-5,3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2x(3x^2-5x+3x-5)
.\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}
2x[(3x^2-5x)+(3x-5)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2x[x(3x-5)+(3x-5)]
.\end{array}
Factoring the $GCF=
(3x-5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
2x[(3x-5)(x+1)]
\\\\=
2x(3x-5)(x+1)
.\end{array}