m^3+6m^2=27m

Solution for m^3+6m^2=27m equation:

Simplifying
m3 + 6m2 = 27m

Reorder the terms:
6m2 + m3 = 27m

Solving
6m2 + m3 = 27m

Solving for variable 'm'.

Reorder the terms:
-27m + 6m2 + m3 = 27m + -27m

Combine like terms: 27m + -27m = 0
-27m + 6m2 + m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-27 + 6m + m2) = 0

Factor a trinomial.
m((-9 + -1m)(3 + -1m)) = 0

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

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(-9 + -1m)' equal to zero and attempt to solve:

Simplifying
-9 + -1m = 0

Solving
-9 + -1m = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1m = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1m = 0 + 9
-1m = 0 + 9

Combine like terms: 0 + 9 = 9
-1m = 9

Divide each side by '-1'.
m = -9

Simplifying
m = -9
Subproblem 3
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {0, -9, 3}