4x^2-xy-18y^2=0

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Solution for 4x^2-xy-18y^2=0 equation: 


Simplifying
4x2 + -1xy + -18y2 = 0

Reorder the terms:
-1xy + 4x2 + -18y2 = 0

Solving
-1xy + 4x2 + -18y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(4x + -9y)' equal to zero and attempt to solve:

Simplifying
4x + -9y = 0

Solving
4x + -9y = 0

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

Add '9y' to each side of the equation.
4x + -9y + 9y = 0 + 9y

Combine like terms: -9y + 9y = 0
4x + 0 = 0 + 9y
4x = 0 + 9y
Remove the zero:
4x = 9y

Divide each side by '4'.
x = 2.25y

Simplifying
x = 2.25y

Subproblem 2
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
Solution
x = {2.25y, -2y}

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