2x^2+xy-36y^2=0

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Solution for 2x^2+xy-36y^2=0 equation: 


Simplifying
2x2 + xy + -36y2 = 0

Reorder the terms:
xy + 2x2 + -36y2 = 0

Solving
xy + 2x2 + -36y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -4y)(2x + 9y) = 0


Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y

Subproblem 2
Set the factor '(2x + 9y)' equal to zero and attempt to solve:

Simplifying
2x + 9y = 0

Solving
2x + 9y = 0

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

Add '-9y' to each side of the equation.
2x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
2x + 0 = 0 + -9y
2x = 0 + -9y
Remove the zero:
2x = -9y

Divide each side by '2'.
x = -4.5y

Simplifying
x = -4.5y
Solution
x = {4y, -4.5y}

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