(r-2)(r^2-2r)=0

Solution for (r-2)(r^2-2r)=0 equation:

Simplifying
(r + -2)(r2 + -2r) = 0

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

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

Multiply (-2 + r) * (-2r + r2)
(-2(-2r + r2) + r(-2r + r2)) = 0
((-2r * -2 + r2 * -2) + r(-2r + r2)) = 0
((4r + -2r2) + r(-2r + r2)) = 0
(4r + -2r2 + (-2r * r + r2 * r)) = 0
(4r + -2r2 + (-2r2 + r3)) = 0

Combine like terms: -2r2 + -2r2 = -4r2
(4r + -4r2 + r3) = 0

Solving
4r + -4r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(4 + -4r + r2) = 0

Factor a trinomial.
r((2 + -1r)(2 + -1r)) = 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 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

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