r^3-72r=-(r^3)

Solution for r^3-72r=-(r^3) equation:

Simplifying
r3 + -72r = -1(r3)

Reorder the terms:
-72r + r3 = -1(r3)

Solving
-72r + r3 = -1r3

Solving for variable 'r'.

Combine like terms: r3 + r3 = 2r3
-72r + 2r3 = -1r3 + r3

Combine like terms: -1r3 + r3 = 0
-72r + 2r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-36 + r2) = 0

Factor a difference between two squares.
2r((6 + r)(-6 + r)) = 0

Ignore the factor 2.
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 '(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
Subproblem 3
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, 6}