#### Answer

$x=\left\{ 1,4 \right\}$

#### Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $
(x+2)(x-7)=-18
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x)+x(-7)+2(x)+2(-7)=-18
\\\\
x^2-7x+2x-14=-18
\\\\
x^2-7x+2x-14+18=0
\\\\
x^2-5x+4=0
.\end{array}
Factoring the above equation, $
x^2-5x+4=0
,$ results to
\begin{array}{l}\require{cancel}
(x-4)(x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(x-4)(x-1)=0
,$ are
\begin{array}{l}\require{cancel}
x-4=0
\\\\
x=4
,\\\\\text{OR}\\\\
x-1=0
\\\\
x=1
.\end{array}
Hence, $
x=\left\{ 1,4 \right\}
.$