(8x^4-2)(8x^4+1)=

Solution for (8x^4-2)(8x^4+1)= equation:

Simplifying
(8x4 + -2)(8x4 + 1) = 0

Reorder the terms:
(-2 + 8x4)(8x4 + 1) = 0

Reorder the terms:
(-2 + 8x4)(1 + 8x4) = 0

Multiply (-2 + 8x4) * (1 + 8x4)
(-2(1 + 8x4) + 8x4 * (1 + 8x4)) = 0
((1 * -2 + 8x4 * -2) + 8x4 * (1 + 8x4)) = 0
((-2 + -16x4) + 8x4 * (1 + 8x4)) = 0
(-2 + -16x4 + (1 * 8x4 + 8x4 * 8x4)) = 0
(-2 + -16x4 + (8x4 + 64x8)) = 0

Combine like terms: -16x4 + 8x4 = -8x4
(-2 + -8x4 + 64x8) = 0

Solving
-2 + -8x4 + 64x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4x4 + 32x8) = 0

Factor a trinomial.
2((-1 + -8x4)(1 + -4x4)) = 0

Factor a difference between two squares.
2((-1 + -8x4)((1 + 2x2)(1 + -2x2))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -8x4)' equal to zero and attempt to solve:

Simplifying
-1 + -8x4 = 0

Solving
-1 + -8x4 = 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 + -8x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x4 = 0 + 1
-8x4 = 0 + 1

Combine like terms: 0 + 1 = 1
-8x4 = 1

Divide each side by '-8'.
x4 = -0.125

Simplifying
x4 = -0.125

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 '(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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
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}