y^4=x^4

Solution for y^4=x^4 equation:

Simplifying
y4 = x4

Solving
y4 = x4

Solving for variable 'y'.

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

Simplifying
y4 = x4

Reorder the terms:
-1x4 + y4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-1x4 + y4 = 0

Factor a difference between two squares.
(x2 + y2)(-1x2 + y2) = 0

Factor a difference between two squares.
(x2 + y2)((x + y)(-1x + y)) = 0

Subproblem 1
Set the factor '(x2 + y2)' equal to zero and attempt to solve:

Simplifying
x2 + y2 = 0

Solving
x2 + y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y2 = 0 + -1x2
y2 = 0 + -1x2
Remove the zero:
y2 = -1x2

Simplifying
y2 = -1x2

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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

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

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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