Answer
$x=1$
Work Step by Step
$(x+2)^{2}=(x-4)^{2}$
Evaluate the powers on both sides:
$x^{2}+4x+4=x^{2}-8x+16$
Since $x^{2}$ is repeated on both sides, it can be removed from the equation
$4x+4=-8x+16$
Take $-8x$ to the left side and $4$ to the right side:
$4x+8x=16-4$
Evaluate the operations on both sides:
$12x=12$
Take $12$ to divide the right side:
$x=\dfrac{12}{12}=1$
$x=1$