(24+18x+8y+6xy)dx-dy=0

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Solution for (24+18x+8y+6xy)dx-dy=0 equation: 


Simplifying
(24 + 18x + 8y + 6xy) * dx + -1dy = 0

Reorder the terms:
(24 + 18x + 6xy + 8y) * dx + -1dy = 0

Reorder the terms for easier multiplication:
dx(24 + 18x + 6xy + 8y) + -1dy = 0
(24 * dx + 18x * dx + 6xy * dx + 8y * dx) + -1dy = 0

Reorder the terms:
(24dx + 8dxy + 18dx2 + 6dx2y) + -1dy = 0
(24dx + 8dxy + 18dx2 + 6dx2y) + -1dy = 0

Solving
24dx + 8dxy + 18dx2 + 6dx2y + -1dy = 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(24x + 8xy + 18x2 + 6x2y + -1y) = 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 '(24x + 8xy + 18x2 + 6x2y + -1y)' equal to zero and attempt to solve:

Simplifying
24x + 8xy + 18x2 + 6x2y + -1y = 0

Solving
24x + 8xy + 18x2 + 6x2y + -1y = 0

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

Add '-24x' to each side of the equation.
24x + 8xy + 18x2 + 6x2y + -24x + -1y = 0 + -24x

Reorder the terms:
24x + -24x + 8xy + 18x2 + 6x2y + -1y = 0 + -24x

Combine like terms: 24x + -24x = 0
0 + 8xy + 18x2 + 6x2y + -1y = 0 + -24x
8xy + 18x2 + 6x2y + -1y = 0 + -24x
Remove the zero:
8xy + 18x2 + 6x2y + -1y = -24x

Add '-8xy' to each side of the equation.
8xy + 18x2 + 6x2y + -8xy + -1y = -24x + -8xy

Reorder the terms:
8xy + -8xy + 18x2 + 6x2y + -1y = -24x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 18x2 + 6x2y + -1y = -24x + -8xy
18x2 + 6x2y + -1y = -24x + -8xy

Add '-18x2' to each side of the equation.
18x2 + 6x2y + -18x2 + -1y = -24x + -8xy + -18x2

Reorder the terms:
18x2 + -18x2 + 6x2y + -1y = -24x + -8xy + -18x2

Combine like terms: 18x2 + -18x2 = 0
0 + 6x2y + -1y = -24x + -8xy + -18x2
6x2y + -1y = -24x + -8xy + -18x2

Add '-6x2y' to each side of the equation.
6x2y + -6x2y + -1y = -24x + -8xy + -18x2 + -6x2y

Combine like terms: 6x2y + -6x2y = 0
0 + -1y = -24x + -8xy + -18x2 + -6x2y
-1y = -24x + -8xy + -18x2 + -6x2y

Add 'y' to each side of the equation.
-1y + y = -24x + -8xy + -18x2 + -6x2y + y

Combine like terms: -1y + y = 0
0 = -24x + -8xy + -18x2 + -6x2y + y

Simplifying
0 = -24x + -8xy + -18x2 + -6x2y + y

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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