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

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


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

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

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

Reorder the terms:
(6dx + dxy + -3dx2) + (x + y + 2) * dy = 0
(6dx + dxy + -3dx2) + (x + y + 2) * dy = 0

Reorder the terms:
6dx + dxy + -3dx2 + (2 + x + y) * dy = 0

Reorder the terms for easier multiplication:
6dx + dxy + -3dx2 + dy(2 + x + y) = 0
6dx + dxy + -3dx2 + (2 * dy + x * dy + y * dy) = 0

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

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

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

Solving
6dx + 2dxy + -3dx2 + 2dy + dy2 = 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(6x + 2xy + -3x2 + 2y + y2) = 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 '(6x + 2xy + -3x2 + 2y + y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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