6r^3+24r^2=72r

Solution for 6r^3+24r^2=72r equation:

Simplifying
6r3 + 24r2 = 72r

Reorder the terms:
24r2 + 6r3 = 72r

Solving
24r2 + 6r3 = 72r

Solving for variable 'r'.

Reorder the terms:
-72r + 24r2 + 6r3 = 72r + -72r

Combine like terms: 72r + -72r = 0
-72r + 24r2 + 6r3 = 0

Factor out the Greatest Common Factor (GCF), '6r'.
6r(-12 + 4r + r2) = 0

Factor a trinomial.
6r((-6 + -1r)(2 + -1r)) = 0

Ignore the factor 6.
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 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 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 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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, -6, 2}