Answer
$(2x+3)(x+2)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
2x^2+7x+6
\end{align*}
has $ac=
2(6)=12
$ and $b=
7
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,4
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
2x^2+3x+4x+6
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(2x^2+3x)+(4x+6)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(2x+3)+2(2x+3)
.\end{align*}
Factoring the $GCF=
(2x+3)
$ of the entire expression above results to
\begin{align*}
(2x+3)(x+2)
.\end{align*}
