(2x+4y+8)dx+(4x+8y-6)dy=0

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Solution for (2x+4y+8)dx+(4x+8y-6)dy=0 equation: 


Simplifying
(2x + 4y + 8) * dx + (4x + 8y + -6) * dy = 0

Reorder the terms:
(8 + 2x + 4y) * dx + (4x + 8y + -6) * dy = 0

Reorder the terms for easier multiplication:
dx(8 + 2x + 4y) + (4x + 8y + -6) * dy = 0
(8 * dx + 2x * dx + 4y * dx) + (4x + 8y + -6) * dy = 0

Reorder the terms:
(8dx + 4dxy + 2dx2) + (4x + 8y + -6) * dy = 0
(8dx + 4dxy + 2dx2) + (4x + 8y + -6) * dy = 0

Reorder the terms:
8dx + 4dxy + 2dx2 + (-6 + 4x + 8y) * dy = 0

Reorder the terms for easier multiplication:
8dx + 4dxy + 2dx2 + dy(-6 + 4x + 8y) = 0
8dx + 4dxy + 2dx2 + (-6 * dy + 4x * dy + 8y * dy) = 0

Reorder the terms:
8dx + 4dxy + 2dx2 + (4dxy + -6dy + 8dy2) = 0
8dx + 4dxy + 2dx2 + (4dxy + -6dy + 8dy2) = 0

Reorder the terms:
8dx + 4dxy + 4dxy + 2dx2 + -6dy + 8dy2 = 0

Combine like terms: 4dxy + 4dxy = 8dxy
8dx + 8dxy + 2dx2 + -6dy + 8dy2 = 0

Solving
8dx + 8dxy + 2dx2 + -6dy + 8dy2 = 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), '2d'.
2d(4x + 4xy + x2 + -3y + 4y2) = 0

Ignore the factor 2.

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 '(4x + 4xy + x2 + -3y + 4y2)' equal to zero and attempt to solve:

Simplifying
4x + 4xy + x2 + -3y + 4y2 = 0

Solving
4x + 4xy + x2 + -3y + 4y2 = 0

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

Add '-4x' to each side of the equation.
4x + 4xy + x2 + -3y + -4x + 4y2 = 0 + -4x

Reorder the terms:
4x + -4x + 4xy + x2 + -3y + 4y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + 4xy + x2 + -3y + 4y2 = 0 + -4x
4xy + x2 + -3y + 4y2 = 0 + -4x
Remove the zero:
4xy + x2 + -3y + 4y2 = -4x

Add '-4xy' to each side of the equation.
4xy + x2 + -3y + -4xy + 4y2 = -4x + -4xy

Reorder the terms:
4xy + -4xy + x2 + -3y + 4y2 = -4x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + x2 + -3y + 4y2 = -4x + -4xy
x2 + -3y + 4y2 = -4x + -4xy

Add '-1x2' to each side of the equation.
x2 + -3y + -1x2 + 4y2 = -4x + -4xy + -1x2

Reorder the terms:
x2 + -1x2 + -3y + 4y2 = -4x + -4xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -3y + 4y2 = -4x + -4xy + -1x2
-3y + 4y2 = -4x + -4xy + -1x2

Add '3y' to each side of the equation.
-3y + 3y + 4y2 = -4x + -4xy + -1x2 + 3y

Combine like terms: -3y + 3y = 0
0 + 4y2 = -4x + -4xy + -1x2 + 3y
4y2 = -4x + -4xy + -1x2 + 3y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -4x + -4xy + -1x2 + 3y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -4x + -4xy + -1x2 + 3y + -4y2

Simplifying
0 = -4x + -4xy + -1x2 + 3y + -4y2

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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