6x^6-3x^4=9x^2

Solution for 6x^6-3x^4=9x^2 equation:

Simplifying
6x6 + -3x4 = 9x2

Reorder the terms:
-3x4 + 6x6 = 9x2

Solving
-3x4 + 6x6 = 9x2

Solving for variable 'x'.

Reorder the terms:
-9x2 + -3x4 + 6x6 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-9x2 + -3x4 + 6x6 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-3 + -1x2 + 2x4) = 0

Factor a trinomial.
3x2((-1 + -1x2)(3 + -2x2)) = 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 '(-1 + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + -1x2 = 0

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

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

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

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

Simplifying
x2 = -1

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 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 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 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {0, -1.224744871, 1.224744871}