Answer
$d=\left\{ -5,8 \right\}$
Work Step by Step
Expressing in the form $ax^2+bx+c=0,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
d(d-3)=40
\\\\
d^2-3d=40
\\\\
d^2-3d-40=0
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
equation
}$
\begin{array}{l}\require{cancel}
d^2-3d-40=0
\end{array} has $c=
-40
$ and $b=
-3
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-8,5
\right\}.$ Using these two numbers, the $\text{
equation
}$ above is equivalent to
\begin{array}{l}\require{cancel}
(d-8)(d+5)=0
.\end{array}
Equating each factor to zero (Zero Product Property), and then isolating the variable, the solutions are $
d=\left\{ -5,8 \right\}
.$
