Answer
$-7$
Work Step by Step
$4^{x-2}=2^{3x+3}\Rightarrow \left( 2^{2}\right) ^{x-2}=2^{3x+3}\Rightarrow 2^{2x-4}=2^{3x+3}\Rightarrow 2x-4=3x+3\Rightarrow x=-7$
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