1=3x^4+2x^2

Solution for 1=3x^4+2x^2 equation:

Simplifying
1 = 3x4 + 2x2

Reorder the terms:
1 = 2x2 + 3x4

Solving
1 = 2x2 + 3x4

Solving for variable 'x'.

Reorder the terms:
1 + -2x2 + -3x4 = 2x2 + -2x2 + 3x4 + -3x4

Combine like terms: 2x2 + -2x2 = 0
1 + -2x2 + -3x4 = 0 + 3x4 + -3x4
1 + -2x2 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
1 + -2x2 + -3x4 = 0

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

Subproblem 1
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}
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.
Solution
x = {-0.577350269, 0.577350269}