2(x^2+y^2)=5xy

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Solution for 2(x^2+y^2)=5xy equation: 


Simplifying
2(x2 + y2) = 5xy
(x2 * 2 + y2 * 2) = 5xy
(2x2 + 2y2) = 5xy

Solving
2x2 + 2y2 = 5xy

Solving for variable 'x'.

Reorder the terms:
-5xy + 2x2 + 2y2 = 5xy + -5xy

Combine like terms: 5xy + -5xy = 0
-5xy + 2x2 + 2y2 = 0

Factor a trinomial.
(x + -2y)(2x + -1y) = 0


Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve:

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y

Subproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {2y, 0.5y}

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