(8x^4-6x^2)+(2x^2-8)(2x^2+8)=

Solution for (8x^4-6x^2)+(2x^2-8)(2x^2+8)= equation:

Simplifying
(8x4 + -6x2) + (2x2 + -8)(2x2 + 8) = 0

Reorder the terms:
(-6x2 + 8x4) + (2x2 + -8)(2x2 + 8) = 0

Remove parenthesis around (-6x2 + 8x4)
-6x2 + 8x4 + (2x2 + -8)(2x2 + 8) = 0

Reorder the terms:
-6x2 + 8x4 + (-8 + 2x2)(2x2 + 8) = 0

Reorder the terms:
-6x2 + 8x4 + (-8 + 2x2)(8 + 2x2) = 0

Multiply (-8 + 2x2) * (8 + 2x2)
-6x2 + 8x4 + (-8(8 + 2x2) + 2x2 * (8 + 2x2)) = 0
-6x2 + 8x4 + ((8 * -8 + 2x2 * -8) + 2x2 * (8 + 2x2)) = 0
-6x2 + 8x4 + ((-64 + -16x2) + 2x2 * (8 + 2x2)) = 0
-6x2 + 8x4 + (-64 + -16x2 + (8 * 2x2 + 2x2 * 2x2)) = 0
-6x2 + 8x4 + (-64 + -16x2 + (16x2 + 4x4)) = 0

Combine like terms: -16x2 + 16x2 = 0
-6x2 + 8x4 + (-64 + 0 + 4x4) = 0
-6x2 + 8x4 + (-64 + 4x4) = 0

Reorder the terms:
-64 + -6x2 + 8x4 + 4x4 = 0

Combine like terms: 8x4 + 4x4 = 12x4
-64 + -6x2 + 12x4 = 0

Solving
-64 + -6x2 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -3x2 + 6x4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-32 + -3x2 + 6x4)' equal to zero and attempt to solve:

Simplifying
-32 + -3x2 + 6x4 = 0

Solving
-32 + -3x2 + 6x4 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-5.333333333 + -0.5x2 + x4 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -0.5x2 + 5.333333333 + x4 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -0.5x2 + x4 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -0.5x2 + x4 = 0 + 5.333333333
-0.5x2 + x4 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-0.5x2 + x4 = 5.333333333

The x term is -0.5x2.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x2 + 0.0625 + x4 = 5.333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x2 + x4 = 5.333333333 + 0.0625

Combine like terms: 5.333333333 + 0.0625 = 5.395833333
0.0625 + -0.5x2 + x4 = 5.395833333

Factor a perfect square on the left side:
(x2 + -0.25)(x2 + -0.25) = 5.395833333

Calculate the square root of the right side: 2.322893311

Break this problem into two subproblems by setting 
(x2 + -0.25) equal to 2.322893311 and -2.322893311.

Subproblem 1
x2 + -0.25 = 2.322893311

Simplifying
x2 + -0.25 = 2.322893311

Reorder the terms:
-0.25 + x2 = 2.322893311

Solving
-0.25 + x2 = 2.322893311

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x2 = 2.322893311 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = 2.322893311 + 0.25
x2 = 2.322893311 + 0.25

Combine like terms: 2.322893311 + 0.25 = 2.572893311
x2 = 2.572893311

Simplifying
x2 = 2.572893311

Take the square root of each side:
x = {-1.604024099, 1.604024099}

Subproblem 2
x2 + -0.25 = -2.322893311

Simplifying
x2 + -0.25 = -2.322893311

Reorder the terms:
-0.25 + x2 = -2.322893311

Solving
-0.25 + x2 = -2.322893311

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x2 = -2.322893311 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = -2.322893311 + 0.25
x2 = -2.322893311 + 0.25

Combine like terms: -2.322893311 + 0.25 = -2.072893311
x2 = -2.072893311

Simplifying
x2 = -2.072893311

Reorder the terms:
2.072893311 + x2 = -2.072893311 + 2.072893311

Combine like terms: -2.072893311 + 2.072893311 = 0.000000000
2.072893311 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.