(X^2)+X=0

Solution for (X^2)+X=0 equation:

Simplifying
(X2) + X = 0
X2 + X = 0

Reorder the terms:
X + X2 = 0

Solving
X + X2 = 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}