Answer
$-(3x+5)(3x+1)$
Work Step by Step
Factoring the negative $GCF=
-1
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-9x^2-18x-5
\\\\=
-(9x^2+18x+5)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-(9x^2+18x+5)
\end{array} has $ac=
9(5)=45
$ and $b=
18
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
15,3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-(9x^2+15x+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}
-[(9x^2+15x)+(3x+5)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-[3x(3x+5)+(3x+5)]
.\end{array}
Factoring the $GCF=
(3x+5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-[(3x+5)(3x+1)]
\\\\=
-(3x+5)(3x+1)
.\end{array}
