Answer
$x=\left\{ -8,0 \right\}$
Work Step by Step
Changing to exponential form, the given expression, $
\log_2[(2x+8)(x+4)]=5
,$
is equivalent to
\begin{array}{l}\require{cancel}
(2x+8)(x+4)=2^5
.\end{array}
Using concepts of quadratic equations, the solution/s to the equation above is/are
\begin{array}{l}\require{cancel}
2x(x)+2x(4)+8(x)+8(4)=32
\\\\
2x^2+8x+8x+32-32=0
\\\\
2x^2+16x=0
\\\\
\dfrac{2x^2+16x}{2}=\dfrac{0}{2}
\\\\
x^2+8x=0
\\\\
x(x+8)=0
.\end{array}
Equating each factor to zero and then solving for the variable, the solutions are $
x=\left\{ -8,0 \right\}
.$
Upon checking, $
x=\left\{ -8,0 \right\}
$ satisfy the original equation.
