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

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


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

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

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

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

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

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

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

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

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

Solving
4dx + 2dxy + dx2 + 8dy + -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(4x + 2xy + x2 + 8y + -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 '(4x + 2xy + x2 + 8y + -8y2)' equal to zero and attempt to solve:

Simplifying
4x + 2xy + x2 + 8y + -8y2 = 0

Solving
4x + 2xy + x2 + 8y + -8y2 = 0

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

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

Reorder the terms:
4x + -4x + 2xy + x2 + 8y + -8y2 = 0 + -4x

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

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

Reorder the terms:
2xy + -2xy + x2 + 8y + -8y2 = -4x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x2 + 8y + -8y2 = -4x + -2xy
x2 + 8y + -8y2 = -4x + -2xy

Add '-1x2' to each side of the equation.
x2 + 8y + -1x2 + -8y2 = -4x + -2xy + -1x2

Reorder the terms:
x2 + -1x2 + 8y + -8y2 = -4x + -2xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 8y + -8y2 = -4x + -2xy + -1x2
8y + -8y2 = -4x + -2xy + -1x2

Add '-8y' to each side of the equation.
8y + -8y + -8y2 = -4x + -2xy + -1x2 + -8y

Combine like terms: 8y + -8y = 0
0 + -8y2 = -4x + -2xy + -1x2 + -8y
-8y2 = -4x + -2xy + -1x2 + -8y

Add '8y2' to each side of the equation.
-8y2 + 8y2 = -4x + -2xy + -1x2 + -8y + 8y2

Combine like terms: -8y2 + 8y2 = 0
0 = -4x + -2xy + -1x2 + -8y + 8y2

Simplifying
0 = -4x + -2xy + -1x2 + -8y + 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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