Answer
The solution set is $\{6,-2\}.$
Work Step by Step
$ 5^{x^{2}-12}=25^{2x}\quad $ ... recognize 25 as $5^{2}$
$ 5^{x^{2}-12}=(5^{2})^{2x}\quad $ ... apply $(a^{m})^{n}=a^{mn}$
$ 5^{x^{2}-12}=5^{4x}\qquad $ ... exponential functions are one to one.
$ x^{2}-12=4x $
$ x^{2}-4x-12=0$
Factor by finding factors of -12 whose sum is -4
$(x-6)(x+2)=0$
Apply the zero product property
$ x-6=0$ or $ x+2=0$
The solution set is $\{6,-2\}.$
