b^2=-b

Solution for b^2=-b equation:

Simplifying
b2 = -1b

Solving
b2 = -1b

Solving for variable 'b'.

Reorder the terms:
b + b2 = -1b + b

Combine like terms: -1b + b = 0
b + b2 = 0

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

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

Simplifying
b = 0

Solving
b = 0

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

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

Simplifying
1 + b = 0

Solving
1 + b = 0

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

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

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

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

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