r(r+6)=0

Solution for r(r+6)=0 equation:

Simplifying
r(r + 6) = 0

Reorder the terms:
r(6 + r) = 0
(6 * r + r * r) = 0
(6r + r2) = 0

Solving
6r + r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(6 + 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 '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {0, -6}