32x^4-2u^4x^4=0

Solution for 32x^4-2u^4x^4=0 equation:

Simplifying
32x4 + -2u4x4 = 0

Reorder the terms:
-2u4x4 + 32x4 = 0

Solving
-2u4x4 + 32x4 = 0

Solving for variable 'u'.

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

Add '-32x4' to each side of the equation.
-2u4x4 + 32x4 + -32x4 = 0 + -32x4

Combine like terms: 32x4 + -32x4 = 0
-2u4x4 + 0 = 0 + -32x4
-2u4x4 = 0 + -32x4
Remove the zero:
-2u4x4 = -32x4

Divide each side by '-2x4'.
u4 = 16

Simplifying
u4 = 16

Reorder the terms:
-16 + u4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + u4 = 0

Factor a difference between two squares.
(4 + u2)(-4 + u2) = 0

Factor a difference between two squares.
(4 + u2)((2 + u)(-2 + u)) = 0

Subproblem 1
Set the factor '(4 + u2)' equal to zero and attempt to solve:

Simplifying
4 + u2 = 0

Solving
4 + u2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + u2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u2 = 0 + -4
u2 = 0 + -4

Combine like terms: 0 + -4 = -4
u2 = -4

Simplifying
u2 = -4

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 '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

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

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Subproblem 3
Set the factor '(-2 + u)' equal to zero and attempt to solve:

Simplifying
-2 + u = 0

Solving
-2 + u = 0

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

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

Combine like terms: -2 + 2 = 0
0 + u = 0 + 2
u = 0 + 2

Combine like terms: 0 + 2 = 2
u = 2

Simplifying
u = 2
Solution
u = {-2, 2}