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

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


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

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

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

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

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

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

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

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

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

Solving
4dx + 2dxy + 2dx2 + -2dy + -2dy2 = 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(2x + xy + x2 + -1y + -1y2) = 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 '(2x + xy + x2 + -1y + -1y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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