Answer
$x=\{ 6,7 \}$
Work Step by Step
Let $z=x+1.$ Then the given equation, $
(x+1)^2-15(x+1)+56=0
$, is equivalent to
\begin{array}{l}\require{cancel}
z^2-15z+56=0
\\\\
(z-7)(z-8)=0
\\\\
z=\{7,8\}
.\end{array}
Since $z=x+1$, then if $z=7$,
\begin{array}{l}\require{cancel}
7=x+1
\\\\
7-1=x
\\\\
6=x
.\end{array}
Since $z=x+1$, then if $z=8$,
\begin{array}{l}\require{cancel}
8=x+1
\\\\
8-1=x
\\\\
7=x
.\end{array}
Hence, $
x=\{ 6,7 \}
.$
