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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
3dxy + 1dy + -2dy2 + dx(-3 + 6x + -4y) = 0
3dxy + 1dy + -2dy2 + (-3 * dx + 6x * dx + -4y * dx) = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = 3x + xy + -6x2 + -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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