4x^4=4x^2+3

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

Simplifying
4x4 = 4x2 + 3

Reorder the terms:
4x4 = 3 + 4x2

Solving
4x4 = 3 + 4x2

Solving for variable 'x'.

Reorder the terms:
-3 + -4x2 + 4x4 = 3 + 4x2 + -3 + -4x2

Reorder the terms:
-3 + -4x2 + 4x4 = 3 + -3 + 4x2 + -4x2

Combine like terms: 3 + -3 = 0
-3 + -4x2 + 4x4 = 0 + 4x2 + -4x2
-3 + -4x2 + 4x4 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + -4x2 + 4x4 = 0

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

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

Simplifying
-1 + -2x2 = 0

Solving
-1 + -2x2 = 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 + -2x2 = 0 + 1

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

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

Divide each side by '-2'.
x2 = -0.5

Simplifying
x2 = -0.5

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 '(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 = {-1.224744871, 1.224744871}