Answer
The solution set is $\left\{-3, 0\right\}$.
Work Step by Step
Factor out $6b$ to obtain:
$$6b(b+3)=0$$
Use the Zero-Product Property by equating each factor to zero, then solving each equation to obtain:
\begin{align*}
6b&=0 &\text{or}& &b+3=0\\
b&=0 &\text{or}& &b=-3\\
\end{align*}
Checking:
\begin{align*}
6(0^2)+18(0)&=0\\
6(0)+0&=0\\
0&\stackrel{\checkmark}=0
\end{align*}
\begin{align*}
6(-3)^2+18(-3)&=0\\
6(9)+(-54)&=0\\
0&\stackrel{\checkmark}=0
\end{align*}
Therefore, the solution set is $\left\{-3, 0\right\}$.
