35x^2+12xy-32y^2=0

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Solution for 35x^2+12xy-32y^2=0 equation: 


Simplifying
35x2 + 12xy + -32y2 = 0

Reorder the terms:
12xy + 35x2 + -32y2 = 0

Solving
12xy + 35x2 + -32y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -4y)(7x + 8y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7x + 8y)' equal to zero and attempt to solve:

Simplifying
7x + 8y = 0

Solving
7x + 8y = 0

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

Add '-8y' to each side of the equation.
7x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
7x + 0 = 0 + -8y
7x = 0 + -8y
Remove the zero:
7x = -8y

Divide each side by '7'.
x = -1.142857143y

Simplifying
x = -1.142857143y
Solution
x = {0.8y, -1.142857143y}

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