z^2-2zw+w^2=0

Solution for z^2-2zw+w^2=0 equation:

Simplifying
z2 + -2zw + w2 = 0

Reorder the terms:
-2wz + w2 + z2 = 0

Solving
-2wz + w2 + z2 = 0

Solving for variable 'w'.

Factor a trinomial.
(w + -1z)(w + -1z) = 0

Subproblem 1
Set the factor '(w + -1z)' equal to zero and attempt to solve:

Simplifying
w + -1z = 0

Solving
w + -1z = 0

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

Add 'z' to each side of the equation.
w + -1z + z = 0 + z

Combine like terms: -1z + z = 0
w + 0 = 0 + z
w = 0 + z
Remove the zero:
w = z

Simplifying
w = z
Subproblem 2
Set the factor '(w + -1z)' equal to zero and attempt to solve:

Simplifying
w + -1z = 0

Solving
w + -1z = 0

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

Add 'z' to each side of the equation.
w + -1z + z = 0 + z

Combine like terms: -1z + z = 0
w + 0 = 0 + z
w = 0 + z
Remove the zero:
w = z

Simplifying
w = z
Solution
w = {z, z}