0=x-x^2

Solution for 0=x-x^2 equation:

Simplifying
0 = x + -1x2

Solving
0 = x + -1x2

Solving for variable 'x'.
Remove the zero:
-1x + x2 = x + -1x2 + -1x + x2

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

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

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

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

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}