(2x+3y+4)dx+(4x+6y+5)dy=0

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Solution for (2x+3y+4)dx+(4x+6y+5)dy=0 equation: 


Simplifying
(2x + 3y + 4) * dx + (4x + 6y + 5) * dy = 0

Reorder the terms:
(4 + 2x + 3y) * dx + (4x + 6y + 5) * dy = 0

Reorder the terms for easier multiplication:
dx(4 + 2x + 3y) + (4x + 6y + 5) * dy = 0
(4 * dx + 2x * dx + 3y * dx) + (4x + 6y + 5) * dy = 0

Reorder the terms:
(4dx + 3dxy + 2dx2) + (4x + 6y + 5) * dy = 0
(4dx + 3dxy + 2dx2) + (4x + 6y + 5) * dy = 0

Reorder the terms:
4dx + 3dxy + 2dx2 + (5 + 4x + 6y) * dy = 0

Reorder the terms for easier multiplication:
4dx + 3dxy + 2dx2 + dy(5 + 4x + 6y) = 0
4dx + 3dxy + 2dx2 + (5 * dy + 4x * dy + 6y * dy) = 0

Reorder the terms:
4dx + 3dxy + 2dx2 + (4dxy + 5dy + 6dy2) = 0
4dx + 3dxy + 2dx2 + (4dxy + 5dy + 6dy2) = 0

Reorder the terms:
4dx + 3dxy + 4dxy + 2dx2 + 5dy + 6dy2 = 0

Combine like terms: 3dxy + 4dxy = 7dxy
4dx + 7dxy + 2dx2 + 5dy + 6dy2 = 0

Solving
4dx + 7dxy + 2dx2 + 5dy + 6dy2 = 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(4x + 7xy + 2x2 + 5y + 6y2) = 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 '(4x + 7xy + 2x2 + 5y + 6y2)' equal to zero and attempt to solve:

Simplifying
4x + 7xy + 2x2 + 5y + 6y2 = 0

Solving
4x + 7xy + 2x2 + 5y + 6y2 = 0

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

Add '-4x' to each side of the equation.
4x + 7xy + 2x2 + 5y + -4x + 6y2 = 0 + -4x

Reorder the terms:
4x + -4x + 7xy + 2x2 + 5y + 6y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + 7xy + 2x2 + 5y + 6y2 = 0 + -4x
7xy + 2x2 + 5y + 6y2 = 0 + -4x
Remove the zero:
7xy + 2x2 + 5y + 6y2 = -4x

Add '-7xy' to each side of the equation.
7xy + 2x2 + 5y + -7xy + 6y2 = -4x + -7xy

Reorder the terms:
7xy + -7xy + 2x2 + 5y + 6y2 = -4x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 2x2 + 5y + 6y2 = -4x + -7xy
2x2 + 5y + 6y2 = -4x + -7xy

Add '-2x2' to each side of the equation.
2x2 + 5y + -2x2 + 6y2 = -4x + -7xy + -2x2

Reorder the terms:
2x2 + -2x2 + 5y + 6y2 = -4x + -7xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 5y + 6y2 = -4x + -7xy + -2x2
5y + 6y2 = -4x + -7xy + -2x2

Add '-5y' to each side of the equation.
5y + -5y + 6y2 = -4x + -7xy + -2x2 + -5y

Combine like terms: 5y + -5y = 0
0 + 6y2 = -4x + -7xy + -2x2 + -5y
6y2 = -4x + -7xy + -2x2 + -5y

Add '-6y2' to each side of the equation.
6y2 + -6y2 = -4x + -7xy + -2x2 + -5y + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = -4x + -7xy + -2x2 + -5y + -6y2

Simplifying
0 = -4x + -7xy + -2x2 + -5y + -6y2

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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