r^2+21r=0

Solution for r^2+21r=0 equation:

Simplifying
r2 + 21r = 0

Reorder the terms:
21r + r2 = 0

Solving
21r + r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(21 + 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 '(21 + r)' equal to zero and attempt to solve:

Simplifying
21 + r = 0

Solving
21 + r = 0

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

Add '-21' to each side of the equation.
21 + -21 + r = 0 + -21

Combine like terms: 21 + -21 = 0
0 + r = 0 + -21
r = 0 + -21

Combine like terms: 0 + -21 = -21
r = -21

Simplifying
r = -21
Solution
r = {0, -21}