Answer
$x=\{ -6,4 \}$
Work Step by Step
Changing to exponential form, the given expression, $
\log_3[(x+5)(x-3)]=2
,$
is equivalent to
\begin{array}{l}\require{cancel}
(x+5)(x-3)=3^2
.\end{array}
Using concepts of quadratic equations, the solution/s to the equation above is/are
\begin{array}{l}\require{cancel}
x(x)+x(-3)+5(x)+5(-3)=9
\\\\
x^2-3x+5x-15-9=0
\\\\
x^2+2x-24=0
\\\\
(x+6)(x-4)=0
.\end{array}
Equating each factor to zero and then solving for the variable, the solutions are $
x=\{ -6,4 \}
.$
