6m^3+54m^2-6m=0

Solution for 6m^3+54m^2-6m=0 equation:

Simplifying
6m3 + 54m2 + -6m = 0

Reorder the terms:
-6m + 54m2 + 6m3 = 0

Solving
-6m + 54m2 + 6m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6m'.
6m(-1 + 9m + m2) = 0

Ignore the factor 6.
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 '(-1 + 9m + m2)' equal to zero and attempt to solve:

Simplifying
-1 + 9m + m2 = 0

Solving
-1 + 9m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 9m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + 9m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9m + m2 = 0 + 1
9m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
9m + m2 = 1

The m term is 9m.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9m + 20.25 + m2 = 1 + 20.25

Reorder the terms:
20.25 + 9m + m2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + 9m + m2 = 21.25

Factor a perfect square on the left side:
(m + 4.5)(m + 4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(m + 4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
m + 4.5 = 4.609772229

Simplifying
m + 4.5 = 4.609772229

Reorder the terms:
4.5 + m = 4.609772229

Solving
4.5 + m = 4.609772229

Solving for variable 'm'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + m = 4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + m = 4.609772229 + -4.5
m = 4.609772229 + -4.5

Combine like terms: 4.609772229 + -4.5 = 0.109772229
m = 0.109772229

Simplifying
m = 0.109772229

Subproblem 2
m + 4.5 = -4.609772229

Simplifying
m + 4.5 = -4.609772229

Reorder the terms:
4.5 + m = -4.609772229

Solving
4.5 + m = -4.609772229

Solving for variable 'm'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + m = -4.609772229 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + m = -4.609772229 + -4.5
m = -4.609772229 + -4.5

Combine like terms: -4.609772229 + -4.5 = -9.109772229
m = -9.109772229

Simplifying
m = -9.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.109772229, -9.109772229}
Solution
m = {0, 0.109772229, -9.109772229}