[(x*x*x*x)-(y*y*y*y)]*[(x*x*x*x)+(y*y*y*y)]=

Solution for [(x*x*x*x)-(y*y*y*y)]*[(x*x*x*x)+(y*y*y*y)]= equation:

Simplifying
[(x * x * x * x) + -1(y * y * y * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply x * x
[(x2 * x * x) + -1(y * y * y * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply x2 * x
[(x3 * x) + -1(y * y * y * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply x3 * x
[(x4) + -1(y * y * y * y)][(x * x * x * x) + (y * y * y * y)] = 0
[x4 + -1(y * y * y * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply y * y
[x4 + -1(y2 * y * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply y2 * y
[x4 + -1(y3 * y)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply y3 * y
[x4 + -1(y4)][(x * x * x * x) + (y * y * y * y)] = 0

Multiply x * x
[x4 + -1y4][(x2 * x * x) + (y * y * y * y)] = 0

Multiply x2 * x
[x4 + -1y4][(x3 * x) + (y * y * y * y)] = 0

Multiply x3 * x
[x4 + -1y4][(x4) + (y * y * y * y)] = 0
[x4 + -1y4][x4 + (y * y * y * y)] = 0

Multiply y * y
[x4 + -1y4][x4 + (y2 * y * y)] = 0

Multiply y2 * y
[x4 + -1y4][x4 + (y3 * y)] = 0

Multiply y3 * y
[x4 + -1y4][x4 + (y4)] = 0
[x4 + -1y4][x4 + y4] = 0

Multiply [x4 + -1y4] * [x4 + y4]
[x4[x4 + y4] + -1y4 * [x4 + y4]] = 0
[[x4 * x4 + y4 * x4] + -1y4 * [x4 + y4]] = 0

Reorder the terms:
[[x4y4 + x8] + -1y4 * [x4 + y4]] = 0
[[x4y4 + x8] + -1y4 * [x4 + y4]] = 0
[x4y4 + x8 + [x4 * -1y4 + y4 * -1y4]] = 0
[x4y4 + x8 + [-1x4y4 + -1y8]] = 0

Reorder the terms:
[x4y4 + -1x4y4 + x8 + -1y8] = 0

Combine like terms: x4y4 + -1x4y4 = 0
[0 + x8 + -1y8] = 0
[x8 + -1y8] = 0

Solving
x8 + -1y8 = 0

Solving for variable 'x'.

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

Add 'y8' to each side of the equation.
x8 + -1y8 + y8 = 0 + y8

Combine like terms: -1y8 + y8 = 0
x8 + 0 = 0 + y8
x8 = 0 + y8
Remove the zero:
x8 = y8

Simplifying
x8 = y8

Combine like terms: y8 + -1y8 = 0
x8 + -1y8 = 0

Factor a difference between two squares.
(x4 + y4)(x4 + -1y4) = 0

Factor a difference between two squares.
(x4 + y4)((x2 + y2)(x2 + -1y2)) = 0

Factor a difference between two squares.
(x4 + y4)((x2 + y2)((x + y)(x + -1y))) = 0

Subproblem 1
Set the factor '(x4 + y4)' equal to zero and attempt to solve:

Simplifying
x4 + y4 = 0

Solving
x4 + y4 = 0

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

Add '-1y4' to each side of the equation.
x4 + y4 + -1y4 = 0 + -1y4

Combine like terms: y4 + -1y4 = 0
x4 + 0 = 0 + -1y4
x4 = 0 + -1y4
Remove the zero:
x4 = -1y4

Simplifying
x4 = -1y4

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 '(x2 + y2)' equal to zero and attempt to solve:

Simplifying
x2 + y2 = 0

Solving
x2 + y2 = 0

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

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

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

Simplifying
x2 = -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Subproblem 4
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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