#### Answer

$x_{1,2}=0,-8$

#### Work Step by Step

$\log _{2}\left( \left( 2x+8\right) \left( x+4\right) \right) =5\Rightarrow \left( 2x+8\right) \left( x+4\right) =2^{5}=32$
$\Rightarrow 2\left( x+4\right) ^{2}=32\Rightarrow \left( x+4\right) =\pm \sqrt {16}=\pm 4\Rightarrow x_{1,2}=0,-8$