14x^2+48xy-32y^2=0

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Solution for 14x^2+48xy-32y^2=0 equation: 


Simplifying
14x2 + 48xy + -32y2 = 0

Reorder the terms:
48xy + 14x2 + -32y2 = 0

Solving
48xy + 14x2 + -32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24xy + 7x2 + -16y2) = 0

Factor a trinomial.
2((7x + -4y)(x + 4y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7x + -4y)' equal to zero and attempt to solve:

Simplifying
7x + -4y = 0

Solving
7x + -4y = 0

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

Add '4y' to each side of the equation.
7x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
7x + 0 = 0 + 4y
7x = 0 + 4y
Remove the zero:
7x = 4y

Divide each side by '7'.
x = 0.5714285714y

Simplifying
x = 0.5714285714y

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

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {0.5714285714y, -4y}

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