32x^2+28xy-15y^2=0

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Solution for 32x^2+28xy-15y^2=0 equation: 


Simplifying
32x2 + 28xy + -15y2 = 0

Reorder the terms:
28xy + 32x2 + -15y2 = 0

Solving
28xy + 32x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8x + -3y)(4x + 5y) = 0


Subproblem 1
Set the factor '(8x + -3y)' equal to zero and attempt to solve:

Simplifying
8x + -3y = 0

Solving
8x + -3y = 0

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

Add '3y' to each side of the equation.
8x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
8x + 0 = 0 + 3y
8x = 0 + 3y
Remove the zero:
8x = 3y

Divide each side by '8'.
x = 0.375y

Simplifying
x = 0.375y

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

Simplifying
4x + 5y = 0

Solving
4x + 5y = 0

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

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

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

Divide each side by '4'.
x = -1.25y

Simplifying
x = -1.25y
Solution
x = {0.375y, -1.25y}

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