2xy=x^2+y^2

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

Simplifying
2xy = x2 + y2

Solving
2xy = x2 + y2

Solving for variable 'x'.

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

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

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

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

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

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

Add '-1y' to each side of the equation.
-1x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1x + 0 = 0 + -1y
-1x = 0 + -1y
Remove the zero:
-1x = -1y

Divide each side by '-1'.
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}