r^3-6r^2=0

Solution for r^3-6r^2=0 equation:

Simplifying
r3 + -6r2 = 0

Reorder the terms:
-6r2 + r3 = 0

Solving
-6r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-6 + r) = 0

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
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}