(4y+2x-5)dx+(6y+4x-1)dy=0

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Solution for (4y+2x-5)dx+(6y+4x-1)dy=0 equation: 


Simplifying
(4y + 2x + -5) * dx + (6y + 4x + -1) * dy = 0

Reorder the terms:
(-5 + 2x + 4y) * dx + (6y + 4x + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(-5 + 2x + 4y) + (6y + 4x + -1) * dy = 0
(-5 * dx + 2x * dx + 4y * dx) + (6y + 4x + -1) * dy = 0

Reorder the terms:
(-5dx + 4dxy + 2dx2) + (6y + 4x + -1) * dy = 0
(-5dx + 4dxy + 2dx2) + (6y + 4x + -1) * dy = 0

Reorder the terms:
-5dx + 4dxy + 2dx2 + (-1 + 4x + 6y) * dy = 0

Reorder the terms for easier multiplication:
-5dx + 4dxy + 2dx2 + dy(-1 + 4x + 6y) = 0
-5dx + 4dxy + 2dx2 + (-1 * dy + 4x * dy + 6y * dy) = 0

Reorder the terms:
-5dx + 4dxy + 2dx2 + (4dxy + -1dy + 6dy2) = 0
-5dx + 4dxy + 2dx2 + (4dxy + -1dy + 6dy2) = 0

Reorder the terms:
-5dx + 4dxy + 4dxy + 2dx2 + -1dy + 6dy2 = 0

Combine like terms: 4dxy + 4dxy = 8dxy
-5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 0

Solving
-5dx + 8dxy + 2dx2 + -1dy + 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(-5x + 8xy + 2x2 + -1y + 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 '(-5x + 8xy + 2x2 + -1y + 6y2)' equal to zero and attempt to solve:

Simplifying
-5x + 8xy + 2x2 + -1y + 6y2 = 0

Solving
-5x + 8xy + 2x2 + -1y + 6y2 = 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 + 2x2 + -1y + 5x + 6y2 = 0 + 5x

Reorder the terms:
-5x + 5x + 8xy + 2x2 + -1y + 6y2 = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + 8xy + 2x2 + -1y + 6y2 = 0 + 5x
8xy + 2x2 + -1y + 6y2 = 0 + 5x
Remove the zero:
8xy + 2x2 + -1y + 6y2 = 5x

Add '-8xy' to each side of the equation.
8xy + 2x2 + -1y + -8xy + 6y2 = 5x + -8xy

Reorder the terms:
8xy + -8xy + 2x2 + -1y + 6y2 = 5x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 2x2 + -1y + 6y2 = 5x + -8xy
2x2 + -1y + 6y2 = 5x + -8xy

Add '-2x2' to each side of the equation.
2x2 + -1y + -2x2 + 6y2 = 5x + -8xy + -2x2

Reorder the terms:
2x2 + -2x2 + -1y + 6y2 = 5x + -8xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y + 6y2 = 5x + -8xy + -2x2
-1y + 6y2 = 5x + -8xy + -2x2

Add 'y' to each side of the equation.
-1y + y + 6y2 = 5x + -8xy + -2x2 + y

Combine like terms: -1y + y = 0
0 + 6y2 = 5x + -8xy + -2x2 + y
6y2 = 5x + -8xy + -2x2 + y

Add '-6y2' to each side of the equation.
6y2 + -6y2 = 5x + -8xy + -2x2 + y + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = 5x + -8xy + -2x2 + y + -6y2

Simplifying
0 = 5x + -8xy + -2x2 + y + -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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