Z^4-625y^4=0

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Solution for Z^4-625y^4=0 equation: 


Simplifying
Z4 + -625y4 = 0

Solving
Z4 + -625y4 = 0

Solving for variable 'Z'.

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

Add '625y4' to each side of the equation.
Z4 + -625y4 + 625y4 = 0 + 625y4

Combine like terms: -625y4 + 625y4 = 0
Z4 + 0 = 0 + 625y4
Z4 = 0 + 625y4
Remove the zero:
Z4 = 625y4

Simplifying
Z4 = 625y4

Combine like terms: 625y4 + -625y4 = 0
Z4 + -625y4 = 0

Factor a difference between two squares.
(Z2 + 25y2)(Z2 + -25y2) = 0

Factor a difference between two squares.
(Z2 + 25y2)((Z + 5y)(Z + -5y)) = 0


Subproblem 1
Set the factor '(Z2 + 25y2)' equal to zero and attempt to solve:

Simplifying
Z2 + 25y2 = 0

Solving
Z2 + 25y2 = 0

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

Add '-25y2' to each side of the equation.
Z2 + 25y2 + -25y2 = 0 + -25y2

Combine like terms: 25y2 + -25y2 = 0
Z2 + 0 = 0 + -25y2
Z2 = 0 + -25y2
Remove the zero:
Z2 = -25y2

Simplifying
Z2 = -25y2

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 '(Z + 5y)' equal to zero and attempt to solve:

Simplifying
Z + 5y = 0

Solving
Z + 5y = 0

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

Add '-5y' to each side of the equation.
Z + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
Z + 0 = 0 + -5y
Z = 0 + -5y
Remove the zero:
Z = -5y

Simplifying
Z = -5y

Subproblem 3
Set the factor '(Z + -5y)' equal to zero and attempt to solve:

Simplifying
Z + -5y = 0

Solving
Z + -5y = 0

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

Add '5y' to each side of the equation.
Z + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
Z + 0 = 0 + 5y
Z = 0 + 5y
Remove the zero:
Z = 5y

Simplifying
Z = 5y
Solution
Z = {-5y, 5y}

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