4x^2(1-x^2)-1=0

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

Simplifying
4x2(1 + -1x2) + -1 = 0
(1 * 4x2 + -1x2 * 4x2) + -1 = 0
(4x2 + -4x4) + -1 = 0

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

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

Solving for variable 'x'.

Factor a trinomial.
(-1 + 2x2)(1 + -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

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
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

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