(4x+3y+1)dx+(3x+2y+1)dy=0

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Solution for (4x+3y+1)dx+(3x+2y+1)dy=0 equation: 


Simplifying
(4x + 3y + 1) * dx + (3x + 2y + 1) * dy = 0

Reorder the terms:
(1 + 4x + 3y) * dx + (3x + 2y + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 4x + 3y) + (3x + 2y + 1) * dy = 0
(1 * dx + 4x * dx + 3y * dx) + (3x + 2y + 1) * dy = 0

Reorder the terms:
(1dx + 3dxy + 4dx2) + (3x + 2y + 1) * dy = 0
(1dx + 3dxy + 4dx2) + (3x + 2y + 1) * dy = 0

Reorder the terms:
1dx + 3dxy + 4dx2 + (1 + 3x + 2y) * dy = 0

Reorder the terms for easier multiplication:
1dx + 3dxy + 4dx2 + dy(1 + 3x + 2y) = 0
1dx + 3dxy + 4dx2 + (1 * dy + 3x * dy + 2y * dy) = 0

Reorder the terms:
1dx + 3dxy + 4dx2 + (3dxy + 1dy + 2dy2) = 0
1dx + 3dxy + 4dx2 + (3dxy + 1dy + 2dy2) = 0

Reorder the terms:
1dx + 3dxy + 3dxy + 4dx2 + 1dy + 2dy2 = 0

Combine like terms: 3dxy + 3dxy = 6dxy
1dx + 6dxy + 4dx2 + 1dy + 2dy2 = 0

Solving
1dx + 6dxy + 4dx2 + 1dy + 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(x + 6xy + 4x2 + y + 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 '(x + 6xy + 4x2 + y + 2y2)' equal to zero and attempt to solve:

Simplifying
x + 6xy + 4x2 + y + 2y2 = 0

Solving
x + 6xy + 4x2 + y + 2y2 = 0

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

Add '-1x' to each side of the equation.
x + 6xy + 4x2 + y + -1x + 2y2 = 0 + -1x

Reorder the terms:
x + -1x + 6xy + 4x2 + y + 2y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 6xy + 4x2 + y + 2y2 = 0 + -1x
6xy + 4x2 + y + 2y2 = 0 + -1x
Remove the zero:
6xy + 4x2 + y + 2y2 = -1x

Add '-6xy' to each side of the equation.
6xy + 4x2 + y + -6xy + 2y2 = -1x + -6xy

Reorder the terms:
6xy + -6xy + 4x2 + y + 2y2 = -1x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 4x2 + y + 2y2 = -1x + -6xy
4x2 + y + 2y2 = -1x + -6xy

Add '-4x2' to each side of the equation.
4x2 + y + -4x2 + 2y2 = -1x + -6xy + -4x2

Reorder the terms:
4x2 + -4x2 + y + 2y2 = -1x + -6xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + y + 2y2 = -1x + -6xy + -4x2
y + 2y2 = -1x + -6xy + -4x2

Add '-1y' to each side of the equation.
y + -1y + 2y2 = -1x + -6xy + -4x2 + -1y

Combine like terms: y + -1y = 0
0 + 2y2 = -1x + -6xy + -4x2 + -1y
2y2 = -1x + -6xy + -4x2 + -1y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x + -6xy + -4x2 + -1y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x + -6xy + -4x2 + -1y + -2y2

Simplifying
0 = -1x + -6xy + -4x2 + -1y + -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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