2x^2+xy=15y^2

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Solution for 2x^2+xy=15y^2 equation: 


Simplifying
2x2 + xy = 15y2

Reorder the terms:
xy + 2x2 = 15y2

Solving
xy + 2x2 = 15y2

Solving for variable 'x'.

Combine like terms: 15y2 + -15y2 = 0
xy + 2x2 + -15y2 = 0

Factor a trinomial.
(2x + -5y)(x + 3y) = 0


Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

Subproblem 2
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
Solution
x = {2.5y, -3y}

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