r^2=-3r

Solution for r^2=-3r equation:

Simplifying
r2 = -3r

Solving
r2 = -3r

Solving for variable 'r'.

Reorder the terms:
3r + r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
3r + r2 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(3 + r) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Solution
r = {0, -3}