35x^2+13xy-12y^2=0

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Solution for 35x^2+13xy-12y^2=0 equation: 


Simplifying
35x2 + 13xy + -12y2 = 0

Reorder the terms:
13xy + 35x2 + -12y2 = 0

Solving
13xy + 35x2 + -12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -3y)(5x + 4y) = 0


Subproblem 1
Set the factor '(7x + -3y)' equal to zero and attempt to solve:

Simplifying
7x + -3y = 0

Solving
7x + -3y = 0

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

Add '3y' to each side of the equation.
7x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
7x + 0 = 0 + 3y
7x = 0 + 3y
Remove the zero:
7x = 3y

Divide each side by '7'.
x = 0.4285714286y

Simplifying
x = 0.4285714286y

Subproblem 2
Set the factor '(5x + 4y)' equal to zero and attempt to solve:

Simplifying
5x + 4y = 0

Solving
5x + 4y = 0

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

Add '-4y' to each side of the equation.
5x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
5x + 0 = 0 + -4y
5x = 0 + -4y
Remove the zero:
5x = -4y

Divide each side by '5'.
x = -0.8y

Simplifying
x = -0.8y
Solution
x = {0.4285714286y, -0.8y}

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