x^4-z^4=0

Solution for x^4-z^4=0 equation:

Simplifying
x4 + -1z4 = 0

Solving
x4 + -1z4 = 0

Solving for variable 'x'.

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

Add 'z4' to each side of the equation.
x4 + -1z4 + z4 = 0 + z4

Combine like terms: -1z4 + z4 = 0
x4 + 0 = 0 + z4
x4 = 0 + z4
Remove the zero:
x4 = z4

Simplifying
x4 = z4

Combine like terms: z4 + -1z4 = 0
x4 + -1z4 = 0

Factor a difference between two squares.
(x2 + z2)(x2 + -1z2) = 0

Factor a difference between two squares.
(x2 + z2)((x + z)(x + -1z)) = 0

Subproblem 1
Set the factor '(x2 + z2)' equal to zero and attempt to solve:

Simplifying
x2 + z2 = 0

Solving
x2 + z2 = 0

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

Add '-1z2' to each side of the equation.
x2 + z2 + -1z2 = 0 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + 0 = 0 + -1z2
x2 = 0 + -1z2
Remove the zero:
x2 = -1z2

Simplifying
x2 = -1z2

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 '(x + z)' equal to zero and attempt to solve:

Simplifying
x + z = 0

Solving
x + z = 0

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

Add '-1z' to each side of the equation.
x + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
x + 0 = 0 + -1z
x = 0 + -1z
Remove the zero:
x = -1z

Simplifying
x = -1z
Subproblem 3
Set the factor '(x + -1z)' equal to zero and attempt to solve:

Simplifying
x + -1z = 0

Solving
x + -1z = 0

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

Add 'z' to each side of the equation.
x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
x + 0 = 0 + z
x = 0 + z
Remove the zero:
x = z

Simplifying
x = z
Solution
x = {-1z, z}