12x^3(x^2-1)=0

Solution for 12x^3(x^2-1)=0 equation:

Simplifying
12x3(x2 + -1) = 0

Reorder the terms:
12x3(-1 + x2) = 0
(-1 * 12x3 + x2 * 12x3) = 0
(-12x3 + 12x5) = 0

Solving
-12x3 + 12x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x3'.
12x3(-1 + x2) = 0

Factor a difference between two squares.
12x3((1 + x)(-1 + x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1, 1}