6p^3-6p=0

Solution for 6p^3-6p=0 equation:

Simplifying
6p3 + -6p = 0

Reorder the terms:
-6p + 6p3 = 0

Solving
-6p + 6p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6p'.
6p(-1 + p2) = 0

Factor a difference between two squares.
6p((1 + p)(-1 + p)) = 0

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

Simplifying
p = 0

Solving
p = 0

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

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

Simplifying
1 + p = 0

Solving
1 + p = 0

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

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

Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1

Combine like terms: 0 + -1 = -1
p = -1

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

Simplifying
-1 + p = 0

Solving
-1 + p = 0

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

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

Combine like terms: -1 + 1 = 0
0 + p = 0 + 1
p = 0 + 1

Combine like terms: 0 + 1 = 1
p = 1

Simplifying
p = 1
Solution
p = {0, -1, 1}