(2x-y+2)dx+(4x-2y-1)dy=0

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Solution for (2x-y+2)dx+(4x-2y-1)dy=0 equation: 


Simplifying
(2x + -1y + 2) * dx + (4x + -2y + -1) * dy = 0

Reorder the terms:
(2 + 2x + -1y) * dx + (4x + -2y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 2x + -1y) + (4x + -2y + -1) * dy = 0
(2 * dx + 2x * dx + -1y * dx) + (4x + -2y + -1) * dy = 0

Reorder the terms:
(2dx + -1dxy + 2dx2) + (4x + -2y + -1) * dy = 0
(2dx + -1dxy + 2dx2) + (4x + -2y + -1) * dy = 0

Reorder the terms:
2dx + -1dxy + 2dx2 + (-1 + 4x + -2y) * dy = 0

Reorder the terms for easier multiplication:
2dx + -1dxy + 2dx2 + dy(-1 + 4x + -2y) = 0
2dx + -1dxy + 2dx2 + (-1 * dy + 4x * dy + -2y * dy) = 0

Reorder the terms:
2dx + -1dxy + 2dx2 + (4dxy + -1dy + -2dy2) = 0
2dx + -1dxy + 2dx2 + (4dxy + -1dy + -2dy2) = 0

Reorder the terms:
2dx + -1dxy + 4dxy + 2dx2 + -1dy + -2dy2 = 0

Combine like terms: -1dxy + 4dxy = 3dxy
2dx + 3dxy + 2dx2 + -1dy + -2dy2 = 0

Solving
2dx + 3dxy + 2dx2 + -1dy + -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), 'd'.
d(2x + 3xy + 2x2 + -1y + -2y2) = 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 + 3xy + 2x2 + -1y + -2y2)' equal to zero and attempt to solve:

Simplifying
2x + 3xy + 2x2 + -1y + -2y2 = 0

Solving
2x + 3xy + 2x2 + -1y + -2y2 = 0

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

Add '-2x' to each side of the equation.
2x + 3xy + 2x2 + -1y + -2x + -2y2 = 0 + -2x

Reorder the terms:
2x + -2x + 3xy + 2x2 + -1y + -2y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 3xy + 2x2 + -1y + -2y2 = 0 + -2x
3xy + 2x2 + -1y + -2y2 = 0 + -2x
Remove the zero:
3xy + 2x2 + -1y + -2y2 = -2x

Add '-3xy' to each side of the equation.
3xy + 2x2 + -1y + -3xy + -2y2 = -2x + -3xy

Reorder the terms:
3xy + -3xy + 2x2 + -1y + -2y2 = -2x + -3xy

Combine like terms: 3xy + -3xy = 0
0 + 2x2 + -1y + -2y2 = -2x + -3xy
2x2 + -1y + -2y2 = -2x + -3xy

Add '-2x2' to each side of the equation.
2x2 + -1y + -2x2 + -2y2 = -2x + -3xy + -2x2

Reorder the terms:
2x2 + -2x2 + -1y + -2y2 = -2x + -3xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y + -2y2 = -2x + -3xy + -2x2
-1y + -2y2 = -2x + -3xy + -2x2

Add 'y' to each side of the equation.
-1y + y + -2y2 = -2x + -3xy + -2x2 + y

Combine like terms: -1y + y = 0
0 + -2y2 = -2x + -3xy + -2x2 + y
-2y2 = -2x + -3xy + -2x2 + y

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

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

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

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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