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

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

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

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

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

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

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

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

Reorder the terms:
-3dx + -2dxy + dx2 + (2dxy + -1dy + dy2) = 0
-3dx + -2dxy + dx2 + (2dxy + -1dy + dy2) = 0

Reorder the terms:
-3dx + -2dxy + 2dxy + dx2 + -1dy + dy2 = 0

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

Solving
-3dx + dx2 + -1dy + dy2 = 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(-3x + x2 + -1y + y2) = 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 '(-3x + x2 + -1y + y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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