n^2=-2n

Solution for n^2=-2n equation:

Simplifying
n2 = -2n

Solving
n2 = -2n

Solving for variable 'n'.

Reorder the terms:
2n + n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
2n + n2 = 0

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

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

Simplifying
n = 0

Solving
n = 0

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

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

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

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

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