32x^4-4x^2-1=0

Solution for 32x^4-4x^2-1=0 equation:

Simplifying
32x4 + -4x2 + -1 = 0

Reorder the terms:
-1 + -4x2 + 32x4 = 0

Solving
-1 + -4x2 + 32x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -8x2)(1 + -4x2) = 0

Factor a difference between two squares.
(-1 + -8x2)((1 + 2x)(1 + -2x)) = 0

Subproblem 1
Set the factor '(-1 + -8x2)' equal to zero and attempt to solve:

Simplifying
-1 + -8x2 = 0

Solving
-1 + -8x2 = 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 + -8x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x2 = 0 + 1
-8x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-8x2 = 1

Divide each side by '-8'.
x2 = -0.125

Simplifying
x2 = -0.125

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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

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

Simplifying
x = -0.5
Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

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

Simplifying
x = 0.5
Solution
x = {-0.5, 0.5}