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

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

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

Reorder the terms:
(-6dx + -1dxy + 3dx2) + (x + y + 2) * dy = 0
(-6dx + -1dxy + 3dx2) + (x + y + 2) * dy = 0

Reorder the terms:
-6dx + -1dxy + 3dx2 + (2 + x + y) * dy = 0

Reorder the terms for easier multiplication:
-6dx + -1dxy + 3dx2 + dy(2 + x + y) = 0
-6dx + -1dxy + 3dx2 + (2 * dy + x * dy + y * dy) = 0

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

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

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

Solving
-6dx + 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 + 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 + 3x2 + 2y + y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = 6x + -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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