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

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


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

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

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

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

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

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

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

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

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

Solving
2dx + 8dxy + 2dx2 + -3dy + 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), 'd'.
d(2x + 8xy + 2x2 + -3y + 8y2) = 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 '(2x + 8xy + 2x2 + -3y + 8y2)' equal to zero and attempt to solve:

Simplifying
2x + 8xy + 2x2 + -3y + 8y2 = 0

Solving
2x + 8xy + 2x2 + -3y + 8y2 = 0

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

Add '-2x' to each side of the equation.
2x + 8xy + 2x2 + -3y + -2x + 8y2 = 0 + -2x

Reorder the terms:
2x + -2x + 8xy + 2x2 + -3y + 8y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 8xy + 2x2 + -3y + 8y2 = 0 + -2x
8xy + 2x2 + -3y + 8y2 = 0 + -2x
Remove the zero:
8xy + 2x2 + -3y + 8y2 = -2x

Add '-8xy' to each side of the equation.
8xy + 2x2 + -3y + -8xy + 8y2 = -2x + -8xy

Reorder the terms:
8xy + -8xy + 2x2 + -3y + 8y2 = -2x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 2x2 + -3y + 8y2 = -2x + -8xy
2x2 + -3y + 8y2 = -2x + -8xy

Add '-2x2' to each side of the equation.
2x2 + -3y + -2x2 + 8y2 = -2x + -8xy + -2x2

Reorder the terms:
2x2 + -2x2 + -3y + 8y2 = -2x + -8xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -3y + 8y2 = -2x + -8xy + -2x2
-3y + 8y2 = -2x + -8xy + -2x2

Add '3y' to each side of the equation.
-3y + 3y + 8y2 = -2x + -8xy + -2x2 + 3y

Combine like terms: -3y + 3y = 0
0 + 8y2 = -2x + -8xy + -2x2 + 3y
8y2 = -2x + -8xy + -2x2 + 3y

Add '-8y2' to each side of the equation.
8y2 + -8y2 = -2x + -8xy + -2x2 + 3y + -8y2

Combine like terms: 8y2 + -8y2 = 0
0 = -2x + -8xy + -2x2 + 3y + -8y2

Simplifying
0 = -2x + -8xy + -2x2 + 3y + -8y2

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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