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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = xy + -3x2 + 2y + 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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