y^2=-y

Solution for y^2=-y equation:

Simplifying
y2 = -1y

Solving
y2 = -1y

Solving for variable 'y'.

Reorder the terms:
y + y2 = -1y + y

Combine like terms: -1y + y = 0
y + y2 = 0

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

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

Simplifying
y = 0

Solving
y = 0

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

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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