Answer
$-3(x+5)(2x+1)$
Work Step by Step
Factoring the $GCF=
-3
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-6x^2-33x-15
\\\\=
-3(2x^2+11x+5)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-3(2x^2+11x+5)
\end{array} has $ac=
2(5)=10
$ and $b=
11
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
10,1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-3(2x^2+10x+1x+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}
-3[(2x^2+10x)+(1x+5)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-3[2x(x+5)+(x+5)]
.\end{array}
Factoring the $GCF=
(x+5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-3[(x+5)(2x+1)]
\\\\=
-3(x+5)(2x+1)
.\end{array}