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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
2dxy + 4dy + 3dy2 + dx(5 + 4x + 6y) = 0
2dxy + 4dy + 3dy2 + (5 * dx + 4x * dx + 6y * dx) = 0

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

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

Combine like terms: 2dxy + 6dxy = 8dxy
5dx + 8dxy + 4dx2 + 4dy + 3dy2 = 0

Solving
5dx + 8dxy + 4dx2 + 4dy + 3dy2 = 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(5x + 8xy + 4x2 + 4y + 3y2) = 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 '(5x + 8xy + 4x2 + 4y + 3y2)' equal to zero and attempt to solve:

Simplifying
5x + 8xy + 4x2 + 4y + 3y2 = 0

Solving
5x + 8xy + 4x2 + 4y + 3y2 = 0

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

Add '-5x' to each side of the equation.
5x + 8xy + 4x2 + 4y + -5x + 3y2 = 0 + -5x

Reorder the terms:
5x + -5x + 8xy + 4x2 + 4y + 3y2 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 8xy + 4x2 + 4y + 3y2 = 0 + -5x
8xy + 4x2 + 4y + 3y2 = 0 + -5x
Remove the zero:
8xy + 4x2 + 4y + 3y2 = -5x

Add '-8xy' to each side of the equation.
8xy + 4x2 + 4y + -8xy + 3y2 = -5x + -8xy

Reorder the terms:
8xy + -8xy + 4x2 + 4y + 3y2 = -5x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 4x2 + 4y + 3y2 = -5x + -8xy
4x2 + 4y + 3y2 = -5x + -8xy

Add '-4x2' to each side of the equation.
4x2 + 4y + -4x2 + 3y2 = -5x + -8xy + -4x2

Reorder the terms:
4x2 + -4x2 + 4y + 3y2 = -5x + -8xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 4y + 3y2 = -5x + -8xy + -4x2
4y + 3y2 = -5x + -8xy + -4x2

Add '-4y' to each side of the equation.
4y + -4y + 3y2 = -5x + -8xy + -4x2 + -4y

Combine like terms: 4y + -4y = 0
0 + 3y2 = -5x + -8xy + -4x2 + -4y
3y2 = -5x + -8xy + -4x2 + -4y

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -5x + -8xy + -4x2 + -4y + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -5x + -8xy + -4x2 + -4y + -3y2

Simplifying
0 = -5x + -8xy + -4x2 + -4y + -3y2

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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