(6x+4y+3)dx+(3x+2y+2)dy=0

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Solution for (6x+4y+3)dx+(3x+2y+2)dy=0 equation: 


Simplifying
(6x + 4y + 3) * dx + (3x + 2y + 2) * dy = 0

Reorder the terms:
(3 + 6x + 4y) * dx + (3x + 2y + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 6x + 4y) + (3x + 2y + 2) * dy = 0
(3 * dx + 6x * dx + 4y * dx) + (3x + 2y + 2) * dy = 0

Reorder the terms:
(3dx + 4dxy + 6dx2) + (3x + 2y + 2) * dy = 0
(3dx + 4dxy + 6dx2) + (3x + 2y + 2) * dy = 0

Reorder the terms:
3dx + 4dxy + 6dx2 + (2 + 3x + 2y) * dy = 0

Reorder the terms for easier multiplication:
3dx + 4dxy + 6dx2 + dy(2 + 3x + 2y) = 0
3dx + 4dxy + 6dx2 + (2 * dy + 3x * dy + 2y * dy) = 0

Reorder the terms:
3dx + 4dxy + 6dx2 + (3dxy + 2dy + 2dy2) = 0
3dx + 4dxy + 6dx2 + (3dxy + 2dy + 2dy2) = 0

Reorder the terms:
3dx + 4dxy + 3dxy + 6dx2 + 2dy + 2dy2 = 0

Combine like terms: 4dxy + 3dxy = 7dxy
3dx + 7dxy + 6dx2 + 2dy + 2dy2 = 0

Solving
3dx + 7dxy + 6dx2 + 2dy + 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(3x + 7xy + 6x2 + 2y + 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 '(3x + 7xy + 6x2 + 2y + 2y2)' equal to zero and attempt to solve:

Simplifying
3x + 7xy + 6x2 + 2y + 2y2 = 0

Solving
3x + 7xy + 6x2 + 2y + 2y2 = 0

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

Add '-3x' to each side of the equation.
3x + 7xy + 6x2 + 2y + -3x + 2y2 = 0 + -3x

Reorder the terms:
3x + -3x + 7xy + 6x2 + 2y + 2y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 7xy + 6x2 + 2y + 2y2 = 0 + -3x
7xy + 6x2 + 2y + 2y2 = 0 + -3x
Remove the zero:
7xy + 6x2 + 2y + 2y2 = -3x

Add '-7xy' to each side of the equation.
7xy + 6x2 + 2y + -7xy + 2y2 = -3x + -7xy

Reorder the terms:
7xy + -7xy + 6x2 + 2y + 2y2 = -3x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 6x2 + 2y + 2y2 = -3x + -7xy
6x2 + 2y + 2y2 = -3x + -7xy

Add '-6x2' to each side of the equation.
6x2 + 2y + -6x2 + 2y2 = -3x + -7xy + -6x2

Reorder the terms:
6x2 + -6x2 + 2y + 2y2 = -3x + -7xy + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + 2y + 2y2 = -3x + -7xy + -6x2
2y + 2y2 = -3x + -7xy + -6x2

Add '-2y' to each side of the equation.
2y + -2y + 2y2 = -3x + -7xy + -6x2 + -2y

Combine like terms: 2y + -2y = 0
0 + 2y2 = -3x + -7xy + -6x2 + -2y
2y2 = -3x + -7xy + -6x2 + -2y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -3x + -7xy + -6x2 + -2y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -3x + -7xy + -6x2 + -2y + -2y2

Simplifying
0 = -3x + -7xy + -6x2 + -2y + -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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