Answer
$(3x+14)(x+2)$
Work Step by Step
Let $z=(x+3)$. Then the given expression, $
3(x+3)^2+2(x+3)-5
$, is equivalent to $
3z^2+2z-5
$.\\
The two numbers whose product is $ac=
3(-5)=-15
$ and whose sum is $b=
2
$ are $\{
5,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3z^2+2z-5
$, is
\begin{array}{l}\require{cancel}
3z^2+5z-3z-5
\\\\=
(3z^2+5z)-(3z+5)
\\\\=
z(3z+5)-(3z+5)
\\\\=
(3z+5)(z-1)
.\end{array}
Since $z=(x+3)$, then,
\begin{array}{l}
(3z+5)(z-1)
\\\\=
(3(x+3)+5)((x+3)-1)
\\\\=
(3x+9+5)(x+3-1)
\\\\=
(3x+14)(x+2)
.\end{array}
