3r^3+6r^2=144r

Solution for 3r^3+6r^2=144r equation:

Simplifying
3r3 + 6r2 = 144r

Reorder the terms:
6r2 + 3r3 = 144r

Solving
6r2 + 3r3 = 144r

Solving for variable 'r'.

Reorder the terms:
-144r + 6r2 + 3r3 = 144r + -144r

Combine like terms: 144r + -144r = 0
-144r + 6r2 + 3r3 = 0

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-48 + 2r + r2) = 0

Factor a trinomial.
3r((-8 + -1r)(6 + -1r)) = 0

Ignore the factor 3.
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 '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 3
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
Solution
r = {0, -8, 6}