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

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


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

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

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

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

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

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

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

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

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

Solving
1dx + -4dxy + 3dx2 + 2dy + 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(x + -4xy + 3x2 + 2y + 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 '(x + -4xy + 3x2 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
x + -4xy + 3x2 + 2y + y2 = 0

Solving
x + -4xy + 3x2 + 2y + y2 = 0

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

Add '-1x' to each side of the equation.
x + -4xy + 3x2 + 2y + -1x + y2 = 0 + -1x

Reorder the terms:
x + -1x + -4xy + 3x2 + 2y + y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + -4xy + 3x2 + 2y + y2 = 0 + -1x
-4xy + 3x2 + 2y + y2 = 0 + -1x
Remove the zero:
-4xy + 3x2 + 2y + y2 = -1x

Add '4xy' to each side of the equation.
-4xy + 3x2 + 2y + 4xy + y2 = -1x + 4xy

Reorder the terms:
-4xy + 4xy + 3x2 + 2y + y2 = -1x + 4xy

Combine like terms: -4xy + 4xy = 0
0 + 3x2 + 2y + y2 = -1x + 4xy
3x2 + 2y + y2 = -1x + 4xy

Add '-3x2' to each side of the equation.
3x2 + 2y + -3x2 + y2 = -1x + 4xy + -3x2

Reorder the terms:
3x2 + -3x2 + 2y + y2 = -1x + 4xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 2y + y2 = -1x + 4xy + -3x2
2y + y2 = -1x + 4xy + -3x2

Add '-2y' to each side of the equation.
2y + -2y + y2 = -1x + 4xy + -3x2 + -2y

Combine like terms: 2y + -2y = 0
0 + y2 = -1x + 4xy + -3x2 + -2y
y2 = -1x + 4xy + -3x2 + -2y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1x + 4xy + -3x2 + -2y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1x + 4xy + -3x2 + -2y + -1y2

Simplifying
0 = -1x + 4xy + -3x2 + -2y + -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}

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