0=r(r+2)

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

Simplifying
0 = r(r + 2)

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

Solving
0 = 2r + r2

Solving for variable 'r'.
Remove the zero:
-2r + -1r2 = 2r + r2 + -2r + -1r2

Reorder the terms:
-2r + -1r2 = 2r + -2r + r2 + -1r2

Combine like terms: 2r + -2r = 0
-2r + -1r2 = 0 + r2 + -1r2
-2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-2r + -1r2 = 0

Factor out the Greatest Common Factor (GCF), '-1r'.
-1r(2 + 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 '(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}