Answer
$\left\{-4i, 4i\right\}$
Work Step by Step
Add $48$ to both sides to obtain:
$$-3r^2=48$$
Divide $-3$ to both sides:
\begin{align*}
r^2&=-16\end{align*}
Take the square root of both sides to obtain:
\begin{align*}
\sqrt{r^2}&=\pm\sqrt{-16}\\
r&=\pm\sqrt{16(-1)}\\
r&=\pm\sqrt{16} \cdot \sqrt{(-1)}\\
r&=\pm 4 \cdot i &\text{(note that $\sqrt{-1}=i$)}\\
r&=\pm 4i
\end{align*}
Checking:
\begin{align*}
-3(-4i)^2-48&=0\\
-3(16i^2)-48&=0\\
-3(16)(-1)-48&=0 &\text{(note that $i^2=-1$)}\\
48-48&=0\\
0&\stackrel{\checkmark}=0
\end{align*}
\begin{align*}
-3(4i)^2-48&=0\\
-3(16i^2)-48&=0\\
-3(16)(-1)-48&=0 &\text{(note that $i^2=-1$)}\\
48-48&=0\\
0&\stackrel{\checkmark}=0
\end{align*}
Thus, the solution set is $\left\{-4i, 4i\right\}$.
