(6x+8y)dx+(16xy-5)dy=0

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Solution for (6x+8y)dx+(16xy-5)dy=0 equation: 


Simplifying
(6x + 8y) * dx + (16xy + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + 8y) + (16xy + -5) * dy = 0
(6x * dx + 8y * dx) + (16xy + -5) * dy = 0

Reorder the terms:
(8dxy + 6dx2) + (16xy + -5) * dy = 0
(8dxy + 6dx2) + (16xy + -5) * dy = 0

Reorder the terms:
8dxy + 6dx2 + (-5 + 16xy) * dy = 0

Reorder the terms for easier multiplication:
8dxy + 6dx2 + dy(-5 + 16xy) = 0
8dxy + 6dx2 + (-5 * dy + 16xy * dy) = 0

Reorder the terms:
8dxy + 6dx2 + (16dxy2 + -5dy) = 0
8dxy + 6dx2 + (16dxy2 + -5dy) = 0

Reorder the terms:
8dxy + 16dxy2 + 6dx2 + -5dy = 0

Solving
8dxy + 16dxy2 + 6dx2 + -5dy = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(8xy + 16xy2 + 6x2 + -5y) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(8xy + 16xy2 + 6x2 + -5y)' equal to zero and attempt to solve:

Simplifying
8xy + 16xy2 + 6x2 + -5y = 0

Solving
8xy + 16xy2 + 6x2 + -5y = 0

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

Add '-8xy' to each side of the equation.
8xy + 16xy2 + 6x2 + -8xy + -5y = 0 + -8xy

Reorder the terms:
8xy + -8xy + 16xy2 + 6x2 + -5y = 0 + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 16xy2 + 6x2 + -5y = 0 + -8xy
16xy2 + 6x2 + -5y = 0 + -8xy
Remove the zero:
16xy2 + 6x2 + -5y = -8xy

Add '-16xy2' to each side of the equation.
16xy2 + 6x2 + -16xy2 + -5y = -8xy + -16xy2

Reorder the terms:
16xy2 + -16xy2 + 6x2 + -5y = -8xy + -16xy2

Combine like terms: 16xy2 + -16xy2 = 0
0 + 6x2 + -5y = -8xy + -16xy2
6x2 + -5y = -8xy + -16xy2

Add '-6x2' to each side of the equation.
6x2 + -6x2 + -5y = -8xy + -16xy2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + -5y = -8xy + -16xy2 + -6x2
-5y = -8xy + -16xy2 + -6x2

Add '5y' to each side of the equation.
-5y + 5y = -8xy + -16xy2 + -6x2 + 5y

Combine like terms: -5y + 5y = 0
0 = -8xy + -16xy2 + -6x2 + 5y

Simplifying
0 = -8xy + -16xy2 + -6x2 + 5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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