0=r(r+6)

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

Simplifying
0 = r(r + 6)

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

Solving
0 = 6r + r2

Solving for variable 'r'.
Remove the zero:
-6r + -1r2 = 6r + r2 + -6r + -1r2

Reorder the terms:
-6r + -1r2 = 6r + -6r + r2 + -1r2

Combine like terms: 6r + -6r = 0
-6r + -1r2 = 0 + r2 + -1r2
-6r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-6r + -1r2 = 0

Factor out the Greatest Common Factor (GCF), '-1r'.
-1r(6 + r) = 0

Ignore the factor -1.
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}