0=3x^4+9x^2+6

Solution for 0=3x^4+9x^2+6 equation:

Simplifying
0 = 3x4 + 9x2 + 6

Reorder the terms:
0 = 6 + 9x2 + 3x4

Solving
0 = 6 + 9x2 + 3x4

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
-3((2 + x2)(1 + x2)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve:

Simplifying
2 + x2 = 0

Solving
2 + x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 0 + -2

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

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

Simplifying
x2 = -2

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

Simplifying
1 + x2 = 0

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

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

Combine like terms: 0 + -1 = -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.

The solution to this equation could not be determined.