(x-2y+1)dx+(4x-3y-6)dy=0

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Solution for (x-2y+1)dx+(4x-3y-6)dy=0 equation: 


Simplifying
(x + -2y + 1) * dx + (4x + -3y + -6) * dy = 0

Reorder the terms:
(1 + x + -2y) * dx + (4x + -3y + -6) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + x + -2y) + (4x + -3y + -6) * dy = 0
(1 * dx + x * dx + -2y * dx) + (4x + -3y + -6) * dy = 0

Reorder the terms:
(1dx + -2dxy + dx2) + (4x + -3y + -6) * dy = 0
(1dx + -2dxy + dx2) + (4x + -3y + -6) * dy = 0

Reorder the terms:
1dx + -2dxy + dx2 + (-6 + 4x + -3y) * dy = 0

Reorder the terms for easier multiplication:
1dx + -2dxy + dx2 + dy(-6 + 4x + -3y) = 0
1dx + -2dxy + dx2 + (-6 * dy + 4x * dy + -3y * dy) = 0

Reorder the terms:
1dx + -2dxy + dx2 + (4dxy + -6dy + -3dy2) = 0
1dx + -2dxy + dx2 + (4dxy + -6dy + -3dy2) = 0

Reorder the terms:
1dx + -2dxy + 4dxy + dx2 + -6dy + -3dy2 = 0

Combine like terms: -2dxy + 4dxy = 2dxy
1dx + 2dxy + dx2 + -6dy + -3dy2 = 0

Solving
1dx + 2dxy + dx2 + -6dy + -3dy2 = 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(x + 2xy + x2 + -6y + -3y2) = 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 '(x + 2xy + x2 + -6y + -3y2)' equal to zero and attempt to solve:

Simplifying
x + 2xy + x2 + -6y + -3y2 = 0

Solving
x + 2xy + x2 + -6y + -3y2 = 0

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

Add '-1x' to each side of the equation.
x + 2xy + x2 + -6y + -1x + -3y2 = 0 + -1x

Reorder the terms:
x + -1x + 2xy + x2 + -6y + -3y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 2xy + x2 + -6y + -3y2 = 0 + -1x
2xy + x2 + -6y + -3y2 = 0 + -1x
Remove the zero:
2xy + x2 + -6y + -3y2 = -1x

Add '-2xy' to each side of the equation.
2xy + x2 + -6y + -2xy + -3y2 = -1x + -2xy

Reorder the terms:
2xy + -2xy + x2 + -6y + -3y2 = -1x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x2 + -6y + -3y2 = -1x + -2xy
x2 + -6y + -3y2 = -1x + -2xy

Add '-1x2' to each side of the equation.
x2 + -6y + -1x2 + -3y2 = -1x + -2xy + -1x2

Reorder the terms:
x2 + -1x2 + -6y + -3y2 = -1x + -2xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -6y + -3y2 = -1x + -2xy + -1x2
-6y + -3y2 = -1x + -2xy + -1x2

Add '6y' to each side of the equation.
-6y + 6y + -3y2 = -1x + -2xy + -1x2 + 6y

Combine like terms: -6y + 6y = 0
0 + -3y2 = -1x + -2xy + -1x2 + 6y
-3y2 = -1x + -2xy + -1x2 + 6y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -1x + -2xy + -1x2 + 6y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -1x + -2xy + -1x2 + 6y + 3y2

Simplifying
0 = -1x + -2xy + -1x2 + 6y + 3y2

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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