algebra 2 question?

Question

thanks guys for anwering my previous problem!
but i forgot to add this one:

Solve.

1)x(x-1)=x

Answer 1

x ² - x = x
x ² - 2x = 0
(x) (x - 2) = 0
x = 0 , x = 2

Answer 2

x=All positive numbers

because
x(x-1)=x
x^2-x=x
x^2=2x
x=2
this may seem like the answer but since you divide by a variable you lose a lot of factors it turns out x also equal all positive numbers not including 0, if you plug in numbers you will see that it works.

Answer 3

x






x^2-x=x
x^2-x-x=0
x^2-2x=0
x(x-2)=0
x=0 or x=2