Answer
Since $x \ne -2$, then $x = 6$
Work Step by Step
$5^{x^{2}-12} = 25^{2x}$
$5^{x^{2}-12} = (5^{2})^{2x}$
$5^{x^{2}-12} = 5^{4x}$
$x^{2} - 12 = 4x$
$x^{2} - 4x - 12 = 0$
$(x-6)(x+2) = 0$
$x = 6, -2$
Since $x \ne -2$, then $x = 6$
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