12(x^5)-72(x^3)-324(x)=0

Solution for 12(x^5)-72(x^3)-324(x)=0 equation:

Simplifying
12(x5) + -72(x3) + -324(x) = 0

Reorder the terms:
-324x + -72x3 + 12x5 = 0

Solving
-324x + -72x3 + 12x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-27 + -6x2 + x4) = 0

Factor a trinomial.
12x((-3 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
12x((-3 + -1x2)((3 + x)(3 + -1x))) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

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