r(r+2)=0

Solution for r(r+2)=0 equation:

Simplifying
r(r + 2) = 0

Reorder the terms:
r(2 + r) = 0
(2 * r + r * r) = 0
(2r + r2) = 0

Solving
2r + r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(2 + 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 '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

Simplifying
r = -2
Solution
r = {0, -2}