Answer
$x=-2$ or, $x=6$
Work Step by Step
Recall the rule that
$a^m=a^n \longrightarrow m=n$ if $a\ne1,a\ne-1$
Applying this rule, we obtain:
$25^{2x}=5^{x^2-12} \\(5^2)^{2x}=5^{x^2-12}\\4x=x^2-12\\x^2-4x-12=0$
This yields a quadratic equation whose factors are:
$(x+2)(x-6)=0$
By the zero property, we have:
$x+2 =0 \implies x=-2$
or
$x-6=0 \implies x=6$
