(2x+y+6)dx+(4x+2y)dy=0

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Solution for (2x+y+6)dx+(4x+2y)dy=0 equation: 


Simplifying
(2x + y + 6) * dx + (4x + 2y) * dy = 0

Reorder the terms:
(6 + 2x + y) * dx + (4x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(6 + 2x + y) + (4x + 2y) * dy = 0
(6 * dx + 2x * dx + y * dx) + (4x + 2y) * dy = 0

Reorder the terms:
(6dx + dxy + 2dx2) + (4x + 2y) * dy = 0
(6dx + dxy + 2dx2) + (4x + 2y) * dy = 0

Reorder the terms for easier multiplication:
6dx + dxy + 2dx2 + dy(4x + 2y) = 0
6dx + dxy + 2dx2 + (4x * dy + 2y * dy) = 0
6dx + dxy + 2dx2 + (4dxy + 2dy2) = 0

Reorder the terms:
6dx + dxy + 4dxy + 2dx2 + 2dy2 = 0

Combine like terms: dxy + 4dxy = 5dxy
6dx + 5dxy + 2dx2 + 2dy2 = 0

Solving
6dx + 5dxy + 2dx2 + 2dy2 = 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 + 5xy + 2x2 + 2y2) = 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 + 5xy + 2x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
6x + 5xy + 2x2 + 2y2 = 0

Solving
6x + 5xy + 2x2 + 2y2 = 0

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

Add '-6x' to each side of the equation.
6x + 5xy + 2x2 + -6x + 2y2 = 0 + -6x

Reorder the terms:
6x + -6x + 5xy + 2x2 + 2y2 = 0 + -6x

Combine like terms: 6x + -6x = 0
0 + 5xy + 2x2 + 2y2 = 0 + -6x
5xy + 2x2 + 2y2 = 0 + -6x
Remove the zero:
5xy + 2x2 + 2y2 = -6x

Add '-5xy' to each side of the equation.
5xy + 2x2 + -5xy + 2y2 = -6x + -5xy

Reorder the terms:
5xy + -5xy + 2x2 + 2y2 = -6x + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 2x2 + 2y2 = -6x + -5xy
2x2 + 2y2 = -6x + -5xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 2y2 = -6x + -5xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2y2 = -6x + -5xy + -2x2
2y2 = -6x + -5xy + -2x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -6x + -5xy + -2x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -6x + -5xy + -2x2 + -2y2

Simplifying
0 = -6x + -5xy + -2x2 + -2y2

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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