Answer
is $\{-2,-1\}$
Work Step by Step
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
x^2+3x+2=0
\end{array} has $c=
2
$ and $b=
3
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
1,2
\right\}.$ Using these two numbers, the factored form of the given $\text{
equation
}$ is
\begin{array}{l}\require{cancel}
(x+1)(x+2)=0
.\end{array}
Equating each factor to zero (Zero Product Property) and solving for the variable result to
\begin{array}{l|r}
x+1=0 & x+2=0
\\
x=-1 & x=-2
\end{array}
Hence, the solution set of the equation $
x^2+3x+2=0
$ is $\{-2,-1\}$.
