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

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


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

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

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

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

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

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

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

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

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

Solving
-1dx + 4dxy + -3dx2 + 3dy + -1dy2 = 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(-1x + 4xy + -3x2 + 3y + -1y2) = 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 '(-1x + 4xy + -3x2 + 3y + -1y2)' equal to zero and attempt to solve:

Simplifying
-1x + 4xy + -3x2 + 3y + -1y2 = 0

Solving
-1x + 4xy + -3x2 + 3y + -1y2 = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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