Answer
$d=-7$, $d= 0$ , $d= 9$.
Work Step by Step
Given \begin{equation}
2 d^3-4 d^2-63 d+124=63 d+124.
\end{equation}
This equation can be best solved by factoring after bringing it to the standard form.
\begin{equation}
\begin{aligned}
2 d^3-4 d^2-63 d+124&=63 d+124\\
2 d^3-4 d^2-63 d&=63 d\\
2 d^3-4 d^2-126 d&=0\\
2d( d^2-2 d-63 )=0.
\end{aligned}
\end{equation} This gives \begin{equation}
\begin{aligned}
d&=0\\
d^2-2 d-63&=0\\
d^2-9d+7d-63&=0\\
d(d-9 )+7(d-9)=0\\
(d+7)(d-9)&= 0\\
\therefore d&= 0 && d= -7 && d= 9.
\end{aligned}
\end{equation} Check \begin{equation}
\begin{aligned}
2\cdot (0)^3-4\cdot (0)^2-63\cdot(0)+124 &\stackrel{?}{=}63 \cdot 0+124\\
124&= 124\ \textbf{True}\\
2\cdot (-7)^3-4\cdot (-7)^2-63\cdot(-7)+124 &\stackrel{?}{=}63\cdot(-7)+124\\
-317&= -317\ \textbf{True}\\
2\cdot (9)^3-4\cdot (9)^2-63\cdot(9)+124 &\stackrel{?}{=}63\cdot 9+124\\
691&= 691\ \textbf{True}
\end{aligned}
\end{equation} The solution is $$d=-7,\quad d= 0,\quad d= 9.$$
