y^4-2y^2z^2+z^4=

Solution for y^4-2y^2z^2+z^4= equation:

Simplifying
y4 + -2y2z2 + z4 = 0

Reorder the terms:
-2y2z2 + y4 + z4 = 0

Solving
-2y2z2 + y4 + z4 = 0

Solving for variable 'y'.

Factor a trinomial.
(y2 + -1z2)(y2 + -1z2) = 0

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

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

Subproblem 1
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 2
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
Subproblem 3
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 4
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, -1z, z}