0=(2x^4-16x^2-91)8x

Solution for 0=(2x^4-16x^2-91)8x equation:

Simplifying
0 = (2x4 + -16x2 + -91) * 8x

Reorder the terms:
0 = (-91 + -16x2 + 2x4) * 8x

Reorder the terms for easier multiplication:
0 = 8x(-91 + -16x2 + 2x4)
0 = (-91 * 8x + -16x2 * 8x + 2x4 * 8x)
0 = (-728x + -128x3 + 16x5)

Solving
0 = -728x + -128x3 + 16x5

Solving for variable 'x'.
Remove the zero:
728x + 128x3 + -16x5 = -728x + -128x3 + 16x5 + 728x + 128x3 + -16x5

Reorder the terms:
728x + 128x3 + -16x5 = -728x + 728x + -128x3 + 128x3 + 16x5 + -16x5

Combine like terms: -728x + 728x = 0
728x + 128x3 + -16x5 = 0 + -128x3 + 128x3 + 16x5 + -16x5
728x + 128x3 + -16x5 = -128x3 + 128x3 + 16x5 + -16x5

Combine like terms: -128x3 + 128x3 = 0
728x + 128x3 + -16x5 = 0 + 16x5 + -16x5
728x + 128x3 + -16x5 = 16x5 + -16x5

Combine like terms: 16x5 + -16x5 = 0
728x + 128x3 + -16x5 = 0

Factor out the Greatest Common Factor (GCF), '8x'.
8x(91 + 16x2 + -2x4) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(91 + 16x2 + -2x4)' equal to zero and attempt to solve:

Simplifying
91 + 16x2 + -2x4 = 0

Solving
91 + 16x2 + -2x4 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-45.5 + -8x2 + x4 = 0

Move the constant term to the right:

Add '45.5' to each side of the equation.
-45.5 + -8x2 + 45.5 + x4 = 0 + 45.5

Reorder the terms:
-45.5 + 45.5 + -8x2 + x4 = 0 + 45.5

Combine like terms: -45.5 + 45.5 = 0.0
0.0 + -8x2 + x4 = 0 + 45.5
-8x2 + x4 = 0 + 45.5

Combine like terms: 0 + 45.5 = 45.5
-8x2 + x4 = 45.5

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = 45.5 + 16

Reorder the terms:
16 + -8x2 + x4 = 45.5 + 16

Combine like terms: 45.5 + 16 = 61.5
16 + -8x2 + x4 = 61.5

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 61.5

Calculate the square root of the right side: 7.842193571

Break this problem into two subproblems by setting 
(x2 + -4) equal to 7.842193571 and -7.842193571.

Subproblem 1
x2 + -4 = 7.842193571

Simplifying
x2 + -4 = 7.842193571

Reorder the terms:
-4 + x2 = 7.842193571

Solving
-4 + x2 = 7.842193571

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = 7.842193571 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 7.842193571 + 4
x2 = 7.842193571 + 4

Combine like terms: 7.842193571 + 4 = 11.842193571
x2 = 11.842193571

Simplifying
x2 = 11.842193571

Take the square root of each side:
x = {-3.441248839, 3.441248839}

Subproblem 2
x2 + -4 = -7.842193571

Simplifying
x2 + -4 = -7.842193571

Reorder the terms:
-4 + x2 = -7.842193571

Solving
-4 + x2 = -7.842193571

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -7.842193571 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -7.842193571 + 4
x2 = -7.842193571 + 4

Combine like terms: -7.842193571 + 4 = -3.842193571
x2 = -3.842193571

Simplifying
x2 = -3.842193571

Reorder the terms:
3.842193571 + x2 = -3.842193571 + 3.842193571

Combine like terms: -3.842193571 + 3.842193571 = 0.000000000
3.842193571 + 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.
Solution
x = {0}