Answer
$x=\{ -7,4 \}$
Work Step by Step
The factored form of the given expression, $
(x-1)(x+4)=24
$, is
\begin{array}{}
x^2+4x-x-4=24
\\\\
x^2+3x-4-24=0
\\\\
x^2+3x-28=0
\\\\
(x+7)(x-4)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x+7=0
\\
x=0-7
\\
x=-7
,\text{ OR}\\\\
x-4=0
\\
x=0+4
\\
x=4
\end{array}
Hence, $
x=\{ -7,4 \}
$.
