Answer
The solution set is $\left\{-4, 1\right\}$.
Work Step by Step
Simplify the equation by multiplying the binomials and adding $24$ to both sides:
\begin{align*}
d(d)+d(-4)+7(d)+(7(-4)+24&=-24+24\\
d^2-4d+7d-28+24&=0\\
d^2+3d-4&=0
\end{align*}
Factor the trinomial:
$$(d+4)(d-1)=0$$
Use the Zero-Product Property by equating each factor to zero.
Then, solve each equation to obtain:
\begin{align*}
d+4&=0 &\text{or}& &d-1=0\\
d&=-4 &\text{or}& &d=1\\
\end{align*}
Checking:
\begin{align*}
(-4+7)(-4-4)&=-24\\
(3)(-8)&=-24\\
-24&\stackrel{\checkmark}=-24
\end{align*}
\begin{align*}
(1+7)(1-4)&=-24\\
(8)(-3)&=-24\\
-24&\stackrel{\checkmark}=-24
\end{align*}
Therefore, the solution set is $\left\{-4, 1\right\}$.