x^2+2y^2=2xy+y^2

Solution for x^2+2y^2=2xy+y^2 equation:

Simplifying
x2 + 2y2 = 2xy + y2

Solving
x2 + 2y2 = 2xy + y2

Solving for variable 'x'.

Reorder the terms:
-2xy + x2 + 2y2 + -1y2 = 2xy + y2 + -2xy + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-2xy + x2 + 1y2 = 2xy + y2 + -2xy + -1y2

Reorder the terms:
-2xy + x2 + 1y2 = 2xy + -2xy + y2 + -1y2

Combine like terms: 2xy + -2xy = 0
-2xy + x2 + 1y2 = 0 + y2 + -1y2
-2xy + x2 + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2xy + x2 + 1y2 = 0

Factor a trinomial.
(x + -1y)(x + -1y) = 0

Subproblem 1
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
Subproblem 2
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 = {y, y}