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

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


Simplifying
(3x + 4y + -5) * dy + -1(2x + 4y + -5) * dx = 0

Reorder the terms:
(-5 + 3x + 4y) * dy + -1(2x + 4y + -5) * dx = 0

Reorder the terms for easier multiplication:
dy(-5 + 3x + 4y) + -1(2x + 4y + -5) * dx = 0
(-5 * dy + 3x * dy + 4y * dy) + -1(2x + 4y + -5) * dx = 0

Reorder the terms:
(3dxy + -5dy + 4dy2) + -1(2x + 4y + -5) * dx = 0
(3dxy + -5dy + 4dy2) + -1(2x + 4y + -5) * dx = 0

Reorder the terms:
3dxy + -5dy + 4dy2 + -1(-5 + 2x + 4y) * dx = 0

Reorder the terms for easier multiplication:
3dxy + -5dy + 4dy2 + -1dx(-5 + 2x + 4y) = 0
3dxy + -5dy + 4dy2 + (-5 * -1dx + 2x * -1dx + 4y * -1dx) = 0

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

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

Combine like terms: 3dxy + -4dxy = -1dxy
5dx + -1dxy + -2dx2 + -5dy + 4dy2 = 0

Solving
5dx + -1dxy + -2dx2 + -5dy + 4dy2 = 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 + -1xy + -2x2 + -5y + 4y2) = 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 + -1xy + -2x2 + -5y + 4y2)' equal to zero and attempt to solve:

Simplifying
5x + -1xy + -2x2 + -5y + 4y2 = 0

Solving
5x + -1xy + -2x2 + -5y + 4y2 = 0

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

Add '-5x' to each side of the equation.
5x + -1xy + -2x2 + -5y + -5x + 4y2 = 0 + -5x

Reorder the terms:
5x + -5x + -1xy + -2x2 + -5y + 4y2 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + -1xy + -2x2 + -5y + 4y2 = 0 + -5x
-1xy + -2x2 + -5y + 4y2 = 0 + -5x
Remove the zero:
-1xy + -2x2 + -5y + 4y2 = -5x

Add 'xy' to each side of the equation.
-1xy + -2x2 + -5y + xy + 4y2 = -5x + xy

Reorder the terms:
-1xy + xy + -2x2 + -5y + 4y2 = -5x + xy

Combine like terms: -1xy + xy = 0
0 + -2x2 + -5y + 4y2 = -5x + xy
-2x2 + -5y + 4y2 = -5x + xy

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

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

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

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

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

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

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

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

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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