(2x^2-3)(2x^2-3)=1

Solution for (2x^2-3)(2x^2-3)=1 equation:

Simplifying
(2x2 + -3)(2x2 + -3) = 1

Reorder the terms:
(-3 + 2x2)(2x2 + -3) = 1

Reorder the terms:
(-3 + 2x2)(-3 + 2x2) = 1

Multiply (-3 + 2x2) * (-3 + 2x2)
(-3(-3 + 2x2) + 2x2 * (-3 + 2x2)) = 1
((-3 * -3 + 2x2 * -3) + 2x2 * (-3 + 2x2)) = 1
((9 + -6x2) + 2x2 * (-3 + 2x2)) = 1
(9 + -6x2 + (-3 * 2x2 + 2x2 * 2x2)) = 1
(9 + -6x2 + (-6x2 + 4x4)) = 1

Combine like terms: -6x2 + -6x2 = -12x2
(9 + -12x2 + 4x4) = 1

Solving
9 + -12x2 + 4x4 = 1

Solving for variable 'x'.

Reorder the terms:
9 + -1 + -12x2 + 4x4 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -12x2 + 4x4 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -12x2 + 4x4 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -3x2 + x4) = 0

Factor a trinomial.
4((1 + -1x2)(2 + -1x2)) = 0

Factor a difference between two squares.
4(((1 + x)(1 + -1x))(2 + -1x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

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

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

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.414213562, 1.414213562, -1, 1}