3x^6-27x^2=0

Solution for 3x^6-27x^2=0 equation:

Simplifying
3x6 + -27x2 = 0

Reorder the terms:
-27x2 + 3x6 = 0

Solving
-27x2 + 3x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-9 + x4) = 0

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

Ignore the factor 3.
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 '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

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

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

Combine like terms: 0 + -3 = -3
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 + x2)' equal to zero and attempt to solve:

Simplifying
-3 + x2 = 0

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

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

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

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {0, -1.732050808, 1.732050808}