k^2=-k

Solution for k^2=-k equation:

Simplifying
k2 = -1k

Solving
k2 = -1k

Solving for variable 'k'.

Reorder the terms:
k + k2 = -1k + k

Combine like terms: -1k + k = 0
k + k2 = 0

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

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

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1
Solution
k = {0, -1}