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}