Question 395137
The process is correct. However you're assuming that {{{x <> 0}}}, since you're dividing by x (this part is the mistake) which is assumed to be non-zero so that the operation is defined. If x = 0, the equation is still true, so x = 0 or x = 1.


The best way to solve this is to move x to the other side to produce


{{{x^2 - x = 0}}}


{{{x(x-1) = 0}}}


x = 0, 1


Or, you could do it like the way you did in the question (assuming {{{x<>0}}}), then do the {{{x = 0}}} case and see if it works. However the first method is more solid.