32x^2+48xy-32y^2=0

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Solution for 32x^2+48xy-32y^2=0 equation: 


Simplifying
32x2 + 48xy + -32y2 = 0

Reorder the terms:
48xy + 32x2 + -32y2 = 0

Solving
48xy + 32x2 + -32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(3xy + 2x2 + -2y2) = 0

Factor a trinomial.
16((2x + -1y)(x + 2y)) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

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 = {0.5y, -2y}

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