q^2=-2q

Solution for q^2=-2q equation:

Simplifying
q2 = -2q

Solving
q2 = -2q

Solving for variable 'q'.

Reorder the terms:
2q + q2 = -2q + 2q

Combine like terms: -2q + 2q = 0
2q + q2 = 0

Factor out the Greatest Common Factor (GCF), 'q'.
q(2 + q) = 0

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

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

Simplifying
2 + q = 0

Solving
2 + q = 0

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

Add '-2' to each side of the equation.
2 + -2 + q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + q = 0 + -2
q = 0 + -2

Combine like terms: 0 + -2 = -2
q = -2

Simplifying
q = -2
Solution
q = {0, -2}