(x-2y-1)dx+(3x-6+2)dy=0

Solution for (x-2y-1)dx+(3x-6+2)dy=0 equation:

Simplifying
(x + -2y + -1) * dx + (3x + -6 + 2) * dy = 0

Reorder the terms:
(-1 + x + -2y) * dx + (3x + -6 + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + x + -2y) + (3x + -6 + 2) * dy = 0
(-1 * dx + x * dx + -2y * dx) + (3x + -6 + 2) * dy = 0

Reorder the terms:
(-1dx + -2dxy + dx2) + (3x + -6 + 2) * dy = 0
(-1dx + -2dxy + dx2) + (3x + -6 + 2) * dy = 0

Reorder the terms:
-1dx + -2dxy + dx2 + (-6 + 2 + 3x) * dy = 0

Combine like terms: -6 + 2 = -4
-1dx + -2dxy + dx2 + (-4 + 3x) * dy = 0

Reorder the terms for easier multiplication:
-1dx + -2dxy + dx2 + dy(-4 + 3x) = 0
-1dx + -2dxy + dx2 + (-4 * dy + 3x * dy) = 0

Reorder the terms:
-1dx + -2dxy + dx2 + (3dxy + -4dy) = 0
-1dx + -2dxy + dx2 + (3dxy + -4dy) = 0

Reorder the terms:
-1dx + -2dxy + 3dxy + dx2 + -4dy = 0

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

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

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

Solving
-1x + xy + x2 + -4y = 0

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

Add 'x' to each side of the equation.
-1x + xy + x2 + x + -4y = 0 + x

Reorder the terms:
-1x + x + xy + x2 + -4y = 0 + x

Combine like terms: -1x + x = 0
0 + xy + x2 + -4y = 0 + x
xy + x2 + -4y = 0 + x
Remove the zero:
xy + x2 + -4y = x

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}