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

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


Simplifying
(x + -4y + -3) * dx + -1(x + -5y + -6) * dy = 0

Reorder the terms:
(-3 + x + -4y) * dx + -1(x + -5y + -6) * dy = 0

Reorder the terms for easier multiplication:
dx(-3 + x + -4y) + -1(x + -5y + -6) * dy = 0
(-3 * dx + x * dx + -4y * dx) + -1(x + -5y + -6) * dy = 0

Reorder the terms:
(-3dx + -4dxy + dx2) + -1(x + -5y + -6) * dy = 0
(-3dx + -4dxy + dx2) + -1(x + -5y + -6) * dy = 0

Reorder the terms:
-3dx + -4dxy + dx2 + -1(-6 + x + -5y) * dy = 0

Reorder the terms for easier multiplication:
-3dx + -4dxy + dx2 + -1dy(-6 + x + -5y) = 0
-3dx + -4dxy + dx2 + (-6 * -1dy + x * -1dy + -5y * -1dy) = 0

Reorder the terms:
-3dx + -4dxy + dx2 + (-1dxy + 6dy + 5dy2) = 0
-3dx + -4dxy + dx2 + (-1dxy + 6dy + 5dy2) = 0

Reorder the terms:
-3dx + -4dxy + -1dxy + dx2 + 6dy + 5dy2 = 0

Combine like terms: -4dxy + -1dxy = -5dxy
-3dx + -5dxy + dx2 + 6dy + 5dy2 = 0

Solving
-3dx + -5dxy + dx2 + 6dy + 5dy2 = 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(-3x + -5xy + x2 + 6y + 5y2) = 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 '(-3x + -5xy + x2 + 6y + 5y2)' equal to zero and attempt to solve:

Simplifying
-3x + -5xy + x2 + 6y + 5y2 = 0

Solving
-3x + -5xy + x2 + 6y + 5y2 = 0

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

Add '3x' to each side of the equation.
-3x + -5xy + x2 + 6y + 3x + 5y2 = 0 + 3x

Reorder the terms:
-3x + 3x + -5xy + x2 + 6y + 5y2 = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + -5xy + x2 + 6y + 5y2 = 0 + 3x
-5xy + x2 + 6y + 5y2 = 0 + 3x
Remove the zero:
-5xy + x2 + 6y + 5y2 = 3x

Add '5xy' to each side of the equation.
-5xy + x2 + 6y + 5xy + 5y2 = 3x + 5xy

Reorder the terms:
-5xy + 5xy + x2 + 6y + 5y2 = 3x + 5xy

Combine like terms: -5xy + 5xy = 0
0 + x2 + 6y + 5y2 = 3x + 5xy
x2 + 6y + 5y2 = 3x + 5xy

Add '-1x2' to each side of the equation.
x2 + 6y + -1x2 + 5y2 = 3x + 5xy + -1x2

Reorder the terms:
x2 + -1x2 + 6y + 5y2 = 3x + 5xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 6y + 5y2 = 3x + 5xy + -1x2
6y + 5y2 = 3x + 5xy + -1x2

Add '-6y' to each side of the equation.
6y + -6y + 5y2 = 3x + 5xy + -1x2 + -6y

Combine like terms: 6y + -6y = 0
0 + 5y2 = 3x + 5xy + -1x2 + -6y
5y2 = 3x + 5xy + -1x2 + -6y

Add '-5y2' to each side of the equation.
5y2 + -5y2 = 3x + 5xy + -1x2 + -6y + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = 3x + 5xy + -1x2 + -6y + -5y2

Simplifying
0 = 3x + 5xy + -1x2 + -6y + -5y2

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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