(2x+3y+8)dx+(4x-y-2)dy=0

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Solution for (2x+3y+8)dx+(4x-y-2)dy=0 equation: 


Simplifying
(2x + 3y + 8) * dx + (4x + -1y + -2) * dy = 0

Reorder the terms:
(8 + 2x + 3y) * dx + (4x + -1y + -2) * dy = 0

Reorder the terms for easier multiplication:
dx(8 + 2x + 3y) + (4x + -1y + -2) * dy = 0
(8 * dx + 2x * dx + 3y * dx) + (4x + -1y + -2) * dy = 0

Reorder the terms:
(8dx + 3dxy + 2dx2) + (4x + -1y + -2) * dy = 0
(8dx + 3dxy + 2dx2) + (4x + -1y + -2) * dy = 0

Reorder the terms:
8dx + 3dxy + 2dx2 + (-2 + 4x + -1y) * dy = 0

Reorder the terms for easier multiplication:
8dx + 3dxy + 2dx2 + dy(-2 + 4x + -1y) = 0
8dx + 3dxy + 2dx2 + (-2 * dy + 4x * dy + -1y * dy) = 0

Reorder the terms:
8dx + 3dxy + 2dx2 + (4dxy + -2dy + -1dy2) = 0
8dx + 3dxy + 2dx2 + (4dxy + -2dy + -1dy2) = 0

Reorder the terms:
8dx + 3dxy + 4dxy + 2dx2 + -2dy + -1dy2 = 0

Combine like terms: 3dxy + 4dxy = 7dxy
8dx + 7dxy + 2dx2 + -2dy + -1dy2 = 0

Solving
8dx + 7dxy + 2dx2 + -2dy + -1dy2 = 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(8x + 7xy + 2x2 + -2y + -1y2) = 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 '(8x + 7xy + 2x2 + -2y + -1y2)' equal to zero and attempt to solve:

Simplifying
8x + 7xy + 2x2 + -2y + -1y2 = 0

Solving
8x + 7xy + 2x2 + -2y + -1y2 = 0

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

Add '-8x' to each side of the equation.
8x + 7xy + 2x2 + -2y + -8x + -1y2 = 0 + -8x

Reorder the terms:
8x + -8x + 7xy + 2x2 + -2y + -1y2 = 0 + -8x

Combine like terms: 8x + -8x = 0
0 + 7xy + 2x2 + -2y + -1y2 = 0 + -8x
7xy + 2x2 + -2y + -1y2 = 0 + -8x
Remove the zero:
7xy + 2x2 + -2y + -1y2 = -8x

Add '-7xy' to each side of the equation.
7xy + 2x2 + -2y + -7xy + -1y2 = -8x + -7xy

Reorder the terms:
7xy + -7xy + 2x2 + -2y + -1y2 = -8x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 2x2 + -2y + -1y2 = -8x + -7xy
2x2 + -2y + -1y2 = -8x + -7xy

Add '-2x2' to each side of the equation.
2x2 + -2y + -2x2 + -1y2 = -8x + -7xy + -2x2

Reorder the terms:
2x2 + -2x2 + -2y + -1y2 = -8x + -7xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -2y + -1y2 = -8x + -7xy + -2x2
-2y + -1y2 = -8x + -7xy + -2x2

Add '2y' to each side of the equation.
-2y + 2y + -1y2 = -8x + -7xy + -2x2 + 2y

Combine like terms: -2y + 2y = 0
0 + -1y2 = -8x + -7xy + -2x2 + 2y
-1y2 = -8x + -7xy + -2x2 + 2y

Add 'y2' to each side of the equation.
-1y2 + y2 = -8x + -7xy + -2x2 + 2y + y2

Combine like terms: -1y2 + y2 = 0
0 = -8x + -7xy + -2x2 + 2y + y2

Simplifying
0 = -8x + -7xy + -2x2 + 2y + y2

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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