I solved x(x-1) = 0 like so:

$$ \left(\frac {1}{x}\right) \* x(x-1)=0 \* \left(\frac1x\right) $$
$$ x-1 = 0$$
$$ (1) + x-1 = 0 + (1)$$
$$ x=1 $$

The correct answer is x = 1 and x = 0, where did I mess up?