Simplifying
x^{2} + x = 0
Reorder the terms:
x + x^{2} = 0
Solving
x + x^{2} = 0
Solving for variable 'x'.
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}