35x^2+3xy-54y^2=0

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Solution for 35x^2+3xy-54y^2=0 equation: 


Simplifying
35x2 + 3xy + -54y2 = 0

Reorder the terms:
3xy + 35x2 + -54y2 = 0

Solving
3xy + 35x2 + -54y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -6y)(7x + 9y) = 0


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

Simplifying
5x + -6y = 0

Solving
5x + -6y = 0

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

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

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

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y

Subproblem 2
Set the factor '(7x + 9y)' equal to zero and attempt to solve:

Simplifying
7x + 9y = 0

Solving
7x + 9y = 0

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

Add '-9y' to each side of the equation.
7x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
7x + 0 = 0 + -9y
7x = 0 + -9y
Remove the zero:
7x = -9y

Divide each side by '7'.
x = -1.285714286y

Simplifying
x = -1.285714286y
Solution
x = {1.2y, -1.285714286y}

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