-x^2=x

Solution for -x^2=x equation:

Simplifying
-1x2 = x

Solving
-1x2 = x

Solving for variable 'x'.

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

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

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

Ignore the factor -1.
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}