Answer
$(x+9)(2x-3)$
Work Step by Step
The two numbers whose product is $ac=
2(-27)=-54
$ and whose sum is $b=
15
$ are $\{
18,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2x^2+15x-27
$, is
\begin{array}{l}\require{cancel}
2x^2+18x-3x-27
\\\\=
(2x^2+18x)-(3x+27)
\\\\=
2x(x+9)-3(x+9)
\\\\=
(x+9)(2x-3)
.\end{array}
