y^4-z^4=0

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

Simplifying
y4 + -1z4 = 0

Solving
y4 + -1z4 = 0

Solving for variable 'y'.

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

Add 'z4' to each side of the equation.
y4 + -1z4 + z4 = 0 + z4

Combine like terms: -1z4 + z4 = 0
y4 + 0 = 0 + z4
y4 = 0 + z4
Remove the zero:
y4 = z4

Simplifying
y4 = z4

Combine like terms: z4 + -1z4 = 0
y4 + -1z4 = 0

Factor a difference between two squares.
(y2 + z2)(y2 + -1z2) = 0

Factor a difference between two squares.
(y2 + z2)((y + z)(y + -1z)) = 0

Subproblem 1
Set the factor '(y2 + z2)' equal to zero and attempt to solve:

Simplifying
y2 + z2 = 0

Solving
y2 + z2 = 0

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

Add '-1z2' to each side of the equation.
y2 + z2 + -1z2 = 0 + -1z2

Combine like terms: z2 + -1z2 = 0
y2 + 0 = 0 + -1z2
y2 = 0 + -1z2
Remove the zero:
y2 = -1z2

Simplifying
y2 = -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 '(y + z)' equal to zero and attempt to solve:

Simplifying
y + z = 0

Solving
y + z = 0

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

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

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

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

Simplifying
y + -1z = 0

Solving
y + -1z = 0

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

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

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

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