(3x-y+2)dx+(9x-3y+1)dy=0

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Solution for (3x-y+2)dx+(9x-3y+1)dy=0 equation: 


Simplifying
(3x + -1y + 2) * dx + (9x + -3y + 1) * dy = 0

Reorder the terms:
(2 + 3x + -1y) * dx + (9x + -3y + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 3x + -1y) + (9x + -3y + 1) * dy = 0
(2 * dx + 3x * dx + -1y * dx) + (9x + -3y + 1) * dy = 0

Reorder the terms:
(2dx + -1dxy + 3dx2) + (9x + -3y + 1) * dy = 0
(2dx + -1dxy + 3dx2) + (9x + -3y + 1) * dy = 0

Reorder the terms:
2dx + -1dxy + 3dx2 + (1 + 9x + -3y) * dy = 0

Reorder the terms for easier multiplication:
2dx + -1dxy + 3dx2 + dy(1 + 9x + -3y) = 0
2dx + -1dxy + 3dx2 + (1 * dy + 9x * dy + -3y * dy) = 0

Reorder the terms:
2dx + -1dxy + 3dx2 + (9dxy + 1dy + -3dy2) = 0
2dx + -1dxy + 3dx2 + (9dxy + 1dy + -3dy2) = 0

Reorder the terms:
2dx + -1dxy + 9dxy + 3dx2 + 1dy + -3dy2 = 0

Combine like terms: -1dxy + 9dxy = 8dxy
2dx + 8dxy + 3dx2 + 1dy + -3dy2 = 0

Solving
2dx + 8dxy + 3dx2 + 1dy + -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(2x + 8xy + 3x2 + y + -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 '(2x + 8xy + 3x2 + y + -3y2)' equal to zero and attempt to solve:

Simplifying
2x + 8xy + 3x2 + y + -3y2 = 0

Solving
2x + 8xy + 3x2 + y + -3y2 = 0

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

Add '-2x' to each side of the equation.
2x + 8xy + 3x2 + y + -2x + -3y2 = 0 + -2x

Reorder the terms:
2x + -2x + 8xy + 3x2 + y + -3y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 8xy + 3x2 + y + -3y2 = 0 + -2x
8xy + 3x2 + y + -3y2 = 0 + -2x
Remove the zero:
8xy + 3x2 + y + -3y2 = -2x

Add '-8xy' to each side of the equation.
8xy + 3x2 + y + -8xy + -3y2 = -2x + -8xy

Reorder the terms:
8xy + -8xy + 3x2 + y + -3y2 = -2x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 3x2 + y + -3y2 = -2x + -8xy
3x2 + y + -3y2 = -2x + -8xy

Add '-3x2' to each side of the equation.
3x2 + y + -3x2 + -3y2 = -2x + -8xy + -3x2

Reorder the terms:
3x2 + -3x2 + y + -3y2 = -2x + -8xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + y + -3y2 = -2x + -8xy + -3x2
y + -3y2 = -2x + -8xy + -3x2

Add '-1y' to each side of the equation.
y + -1y + -3y2 = -2x + -8xy + -3x2 + -1y

Combine like terms: y + -1y = 0
0 + -3y2 = -2x + -8xy + -3x2 + -1y
-3y2 = -2x + -8xy + -3x2 + -1y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -2x + -8xy + -3x2 + -1y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -2x + -8xy + -3x2 + -1y + 3y2

Simplifying
0 = -2x + -8xy + -3x2 + -1y + 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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