Answer
$x=\{2,7\}$
Work Step by Step
Let $z=(x-3)$. Then the given expression, $(x-3)^2-3(x-3)-4=0$ is equivalent to
\begin{array}{l}\require{cancel}
z^2-3z-4=0\\
(z-4)(z+1)=0\\
z=\{-1,4\}
.\end{array}
Using $z=-1$, then,
\begin{array}{l}
x-3=-1\\
x=2
.\end{array}
Using $z=4$, then,
\begin{array}{l}
x-3=4\\
x=7
.\end{array}
Hence, $
x=\{2,7\}
.$