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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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