(8x^2+3)(8x^2-3)-(8x^2-1)=22

Solution for (8x^2+3)(8x^2-3)-(8x^2-1)=22 equation:

Simplifying
(8x2 + 3)(8x2 + -3) + -1(8x2 + -1) = 22

Reorder the terms:
(3 + 8x2)(8x2 + -3) + -1(8x2 + -1) = 22

Reorder the terms:
(3 + 8x2)(-3 + 8x2) + -1(8x2 + -1) = 22

Multiply (3 + 8x2) * (-3 + 8x2)
(3(-3 + 8x2) + 8x2 * (-3 + 8x2)) + -1(8x2 + -1) = 22
((-3 * 3 + 8x2 * 3) + 8x2 * (-3 + 8x2)) + -1(8x2 + -1) = 22
((-9 + 24x2) + 8x2 * (-3 + 8x2)) + -1(8x2 + -1) = 22
(-9 + 24x2 + (-3 * 8x2 + 8x2 * 8x2)) + -1(8x2 + -1) = 22
(-9 + 24x2 + (-24x2 + 64x4)) + -1(8x2 + -1) = 22

Combine like terms: 24x2 + -24x2 = 0
(-9 + 0 + 64x4) + -1(8x2 + -1) = 22
(-9 + 64x4) + -1(8x2 + -1) = 22

Reorder the terms:
-9 + 64x4 + -1(-1 + 8x2) = 22
-9 + 64x4 + (-1 * -1 + 8x2 * -1) = 22
-9 + 64x4 + (1 + -8x2) = 22

Reorder the terms:
-9 + 1 + -8x2 + 64x4 = 22

Combine like terms: -9 + 1 = -8
-8 + -8x2 + 64x4 = 22

Solving
-8 + -8x2 + 64x4 = 22

Solving for variable 'x'.

Reorder the terms:
-8 + -22 + -8x2 + 64x4 = 22 + -22

Combine like terms: -8 + -22 = -30
-30 + -8x2 + 64x4 = 22 + -22

Combine like terms: 22 + -22 = 0
-30 + -8x2 + 64x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4x2 + 32x4) = 0

Factor a trinomial.
2((-5 + -8x2)(3 + -4x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -8x2)' equal to zero and attempt to solve:

Simplifying
-5 + -8x2 = 0

Solving
-5 + -8x2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -8x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x2 = 0 + 5
-8x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-8x2 = 5

Divide each side by '-8'.
x2 = -0.625

Simplifying
x2 = -0.625

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 + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x2 = 0

Solving
3 + -4x2 = 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 + -4x2 = 0 + -3

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

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

Divide each side by '-4'.
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Solution
x = {-0.866025404, 0.866025404}