6x^2+xy=5y^2

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Solution for 6x^2+xy=5y^2 equation: 


Simplifying
6x2 + xy = 5y2

Reorder the terms:
xy + 6x2 = 5y2

Solving
xy + 6x2 = 5y2

Solving for variable 'x'.

Combine like terms: 5y2 + -5y2 = 0
xy + 6x2 + -5y2 = 0

Factor a trinomial.
(6x + -5y)(x + y) = 0


Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve:

Simplifying
6x + -5y = 0

Solving
6x + -5y = 0

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

Add '5y' to each side of the equation.
6x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
6x + 0 = 0 + 5y
6x = 0 + 5y
Remove the zero:
6x = 5y

Divide each side by '6'.
x = 0.8333333333y

Simplifying
x = 0.8333333333y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {0.8333333333y, -1y}

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