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

Solution for x^2-x(2-x)=0 equation:

Simplifying
x2 + -1x(2 + -1x) = 0
x2 + (2 * -1x + -1x * -1x) = 0
x2 + (-2x + 1x2) = 0

Reorder the terms:
-2x + x2 + 1x2 = 0

Combine like terms: x2 + 1x2 = 2x2
-2x + 2x2 = 0

Solving
-2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}