Answer
$-(x-3)(2x+5)$
Work Step by Step
Rearranging the terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
-2x^2+15+x
\\\\=
-2x^2+x+15
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-2x^2+x+15
\end{array} has $ac=
-2(15)=-30
$ and $b=
1
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
6,-5
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-2x^2+6x-5x+15
.\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^2+6x)-(5x-15)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-2x(x-3)-5(x-3)
.\end{array}
Factoring the $GCF=
(x-3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x-3)(-2x-5)
\\\\=
-(x-3)(2x+5)
.\end{array}
