3(x^2+y^2)=10xy

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Solution for 3(x^2+y^2)=10xy equation: 


Simplifying
3(x2 + y2) = 10xy
(x2 * 3 + y2 * 3) = 10xy
(3x2 + 3y2) = 10xy

Solving
3x2 + 3y2 = 10xy

Solving for variable 'x'.

Reorder the terms:
-10xy + 3x2 + 3y2 = 10xy + -10xy

Combine like terms: 10xy + -10xy = 0
-10xy + 3x2 + 3y2 = 0

Factor a trinomial.
(x + -3y)(3x + -1y) = 0


Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve:

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '3y' to each side of the equation.
x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y

Subproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {3y, 0.3333333333y}

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