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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -2x + xy + 6y + 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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