Answer
$x_{1}=4;x_{2}=-6$
Work Step by Step
$\log _{3}\left[ \left( x+5\right) \left( x-3\right) \right] =2\Rightarrow \left( x+5\right) \left( x-3\right) =3^{2}$
$ \Rightarrow x^{2}+2x-15=9\Rightarrow x^{2}+2x-24=0$
$\Rightarrow x^{2}+2x+1-25=0\Rightarrow \left( x+1\right) ^{2}-5^{2}=0\Rightarrow \left( x+1-5\right) \left( x+1+5\right) =0$
$\Rightarrow \left( x-4\right) \left( x+6\right) =0\Rightarrow x_{1}=4;x_{2}=-6$