(1-2x^2)(1+2x^2)=0

Solution for (1-2x^2)(1+2x^2)=0 equation:

Simplifying
(1 + -2x2)(1 + 2x2) = 0

Multiply (1 + -2x2) * (1 + 2x2)
(1(1 + 2x2) + -2x2 * (1 + 2x2)) = 0
((1 * 1 + 2x2 * 1) + -2x2 * (1 + 2x2)) = 0
((1 + 2x2) + -2x2 * (1 + 2x2)) = 0
(1 + 2x2 + (1 * -2x2 + 2x2 * -2x2)) = 0
(1 + 2x2 + (-2x2 + -4x4)) = 0

Combine like terms: 2x2 + -2x2 = 0
(1 + 0 + -4x4) = 0
(1 + -4x4) = 0

Solving
1 + -4x4 = 0

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + -4x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x4 = 0 + -1
-4x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x4 = -1

Divide each side by '-4'.
x4 = 0.25

Simplifying
x4 = 0.25

Reorder the terms:
-0.25 + x4 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + x4 = 0.00

Factor a difference between two squares.
(0.5 + x2)(-0.5 + x2) = 0.00

Subproblem 1
Set the factor '(0.5 + x2)' equal to zero and attempt to solve:

Simplifying
0.5 + x2 = 0

Solving
0.5 + x2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 0 + -0.5
x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
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 '(-0.5 + x2)' equal to zero and attempt to solve:

Simplifying
-0.5 + x2 = 0

Solving
-0.5 + x2 = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0 + 0.5
x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {-0.707106781, 0.707106781}