18x^6-2x^2=0

Solution for 18x^6-2x^2=0 equation:

Simplifying
18x6 + -2x2 = 0

Reorder the terms:
-2x2 + 18x6 = 0

Solving
-2x2 + 18x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-1 + 9x4) = 0

Factor a difference between two squares.
2x2((1 + 3x2)(-1 + 3x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + 3x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x2 = 0

Solving
1 + 3x2 = 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 + 3x2 = 0 + -1

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

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

Divide each side by '3'.
x2 = -0.3333333333

Simplifying
x2 = -0.3333333333

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 '(-1 + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 3x2 = 0

Solving
-1 + 3x2 = 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 + 3x2 = 0 + 1

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

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

Divide each side by '3'.
x2 = 0.3333333333

Simplifying
x2 = 0.3333333333

Take the square root of each side:
x = {-0.577350269, 0.577350269}
Solution
x = {0, -0.577350269, 0.577350269}