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

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


Simplifying
(2y2 + 4x + 8) * dx + (4xy + -3y + 2) * dy = 0

Reorder the terms:
(8 + 4x + 2y2) * dx + (4xy + -3y + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(8 + 4x + 2y2) + (4xy + -3y + 2) * dy = 0
(8 * dx + 4x * dx + 2y2 * dx) + (4xy + -3y + 2) * dy = 0

Reorder the terms:
(8dx + 2dxy2 + 4dx2) + (4xy + -3y + 2) * dy = 0
(8dx + 2dxy2 + 4dx2) + (4xy + -3y + 2) * dy = 0

Reorder the terms:
8dx + 2dxy2 + 4dx2 + (2 + 4xy + -3y) * dy = 0

Reorder the terms for easier multiplication:
8dx + 2dxy2 + 4dx2 + dy(2 + 4xy + -3y) = 0
8dx + 2dxy2 + 4dx2 + (2 * dy + 4xy * dy + -3y * dy) = 0

Reorder the terms:
8dx + 2dxy2 + 4dx2 + (4dxy2 + 2dy + -3dy2) = 0
8dx + 2dxy2 + 4dx2 + (4dxy2 + 2dy + -3dy2) = 0

Reorder the terms:
8dx + 2dxy2 + 4dxy2 + 4dx2 + 2dy + -3dy2 = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
8dx + 6dxy2 + 4dx2 + 2dy + -3dy2 = 0

Solving
8dx + 6dxy2 + 4dx2 + 2dy + -3dy2 = 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 + 6xy2 + 4x2 + 2y + -3y2) = 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 + 6xy2 + 4x2 + 2y + -3y2)' equal to zero and attempt to solve:

Simplifying
8x + 6xy2 + 4x2 + 2y + -3y2 = 0

Solving
8x + 6xy2 + 4x2 + 2y + -3y2 = 0

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

Add '-8x' to each side of the equation.
8x + 6xy2 + 4x2 + 2y + -8x + -3y2 = 0 + -8x

Reorder the terms:
8x + -8x + 6xy2 + 4x2 + 2y + -3y2 = 0 + -8x

Combine like terms: 8x + -8x = 0
0 + 6xy2 + 4x2 + 2y + -3y2 = 0 + -8x
6xy2 + 4x2 + 2y + -3y2 = 0 + -8x
Remove the zero:
6xy2 + 4x2 + 2y + -3y2 = -8x

Add '-6xy2' to each side of the equation.
6xy2 + 4x2 + 2y + -6xy2 + -3y2 = -8x + -6xy2

Reorder the terms:
6xy2 + -6xy2 + 4x2 + 2y + -3y2 = -8x + -6xy2

Combine like terms: 6xy2 + -6xy2 = 0
0 + 4x2 + 2y + -3y2 = -8x + -6xy2
4x2 + 2y + -3y2 = -8x + -6xy2

Add '-4x2' to each side of the equation.
4x2 + 2y + -4x2 + -3y2 = -8x + -6xy2 + -4x2

Reorder the terms:
4x2 + -4x2 + 2y + -3y2 = -8x + -6xy2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 2y + -3y2 = -8x + -6xy2 + -4x2
2y + -3y2 = -8x + -6xy2 + -4x2

Add '-2y' to each side of the equation.
2y + -2y + -3y2 = -8x + -6xy2 + -4x2 + -2y

Combine like terms: 2y + -2y = 0
0 + -3y2 = -8x + -6xy2 + -4x2 + -2y
-3y2 = -8x + -6xy2 + -4x2 + -2y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -8x + -6xy2 + -4x2 + -2y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -8x + -6xy2 + -4x2 + -2y + 3y2

Simplifying
0 = -8x + -6xy2 + -4x2 + -2y + 3y2

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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