25x^4-25y^4=

Solution for 25x^4-25y^4= equation:

Simplifying
25x4 + -25y4 = 0

Solving
25x4 + -25y4 = 0

Solving for variable 'x'.

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

Add '25y4' to each side of the equation.
25x4 + -25y4 + 25y4 = 0 + 25y4

Combine like terms: -25y4 + 25y4 = 0
25x4 + 0 = 0 + 25y4
25x4 = 0 + 25y4
Remove the zero:
25x4 = 25y4

Divide each side by '25'.
x4 = y4

Simplifying
x4 = y4

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

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

Factor a difference between two squares.
(x2 + y2)((x + y)(x + -1y)) = 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 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 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 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 3
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}