6c^3-54c=0

Solution for 6c^3-54c=0 equation:

Simplifying
6c3 + -54c = 0

Reorder the terms:
-54c + 6c3 = 0

Solving
-54c + 6c3 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6c'.
6c(-9 + c2) = 0

Factor a difference between two squares.
6c((3 + c)(-3 + c)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

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

Simplifying
c = 0
Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

Solving
3 + c = 0

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

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

Combine like terms: 3 + -3 = 0
0 + c = 0 + -3
c = 0 + -3

Combine like terms: 0 + -3 = -3
c = -3

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

Simplifying
-3 + c = 0

Solving
-3 + c = 0

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

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

Combine like terms: -3 + 3 = 0
0 + c = 0 + 3
c = 0 + 3

Combine like terms: 0 + 3 = 3
c = 3

Simplifying
c = 3
Solution
c = {0, -3, 3}