Answer
The real solution set is {-1,3}.
Work Step by Step
$|x^2-2x|=3$
$x^2-2x=3$ or $x^2-2x=-3$
$x^2-2x-3=0$ or $x^2-2x+3=0$
$(x-3)(x+1)=0$ or $x=\frac{2+\sqrt {4-12}}{2}$ or $x=\frac{2-\sqrt {4-12}}{2}$
$(x-3)=0$ or $(x+1)=0 $ or $x=\frac{2+\sqrt {-8}}{2}$ or $x=\frac{2-\sqrt {-8}}{2}$
$x=3 $ or $x=-1$ or $x=\frac{2+2i\sqrt {2}}{2}=1+i\sqrt
2$
or $x=\frac{2-2i\sqrt {2}}{2}=1-i\sqrt 2$
The real solution set is {-1,3}