Answer
$x=0$
Work Step by Step
We rewrite the 25 on the right side, so that the base is 5 on both sides.
$5^{2+2x}=25
\\5^{2+2x}=5^2$
Then we set the exponents equal, because the two sides are equal only if the powers are equal too:
$2+2x=2$
$2x=2-2$
$2x=0
\\x=0$
