Answer
The solutions are $m=-2$ and $m=-1$.
Work Step by Step
To factor the polynomial $m^{2}+bm+c$, we need to find two numbers $p$ and $q$ such that $p+q=b$ and $pq=c$.
In this case, $b=3$ and $c=2$.
$\implies p=2$ and $q=1$.
Then, $m^{2}+3m+2=(m+p)(m+q)=(m+2)(m+1)$
$m^{2}+3m+2=0\implies (m+2)(m+1)=0$
$\implies m+2=0$ or $m+1=0$
$\implies m=-2$ or $m=-1$
The solutions are $m=-2$ and $m=-1$.
