Answer
The solution set is {$-2,0$}
Work Step by Step
$|x^2-2x|=|x^2+6x|$
$x^2-2x=x^2+6x$ or $x^2-2x=-1(x^2+6x)$
$x^2-2x-x^2-6x=0$ or $x^2-2x+x^2+6x=0$
$-8x=0$ or $2x^2+4x=0$
$x=0$ or $2x(x+2)=0$
$x=0$ or $2x=0$ or $x+2=0$
$x=0$ or $x=0$ or $x=-2$
The solution set is {$-2,0$}