(12-6y+e-3x)dx-2dy=0

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Solution for (12-6y+e-3x)dx-2dy=0 equation: 


Simplifying
(12 + -6y + e + -3x) * dx + -2dy = 0

Reorder the terms:
(12 + e + -3x + -6y) * dx + -2dy = 0

Reorder the terms for easier multiplication:
dx(12 + e + -3x + -6y) + -2dy = 0
(12 * dx + e * dx + -3x * dx + -6y * dx) + -2dy = 0

Reorder the terms:
(dex + 12dx + -6dxy + -3dx2) + -2dy = 0
(dex + 12dx + -6dxy + -3dx2) + -2dy = 0

Solving
dex + 12dx + -6dxy + -3dx2 + -2dy = 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(ex + 12x + -6xy + -3x2 + -2y) = 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 '(ex + 12x + -6xy + -3x2 + -2y)' equal to zero and attempt to solve:

Simplifying
ex + 12x + -6xy + -3x2 + -2y = 0

Solving
ex + 12x + -6xy + -3x2 + -2y = 0

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

Add '-1ex' to each side of the equation.
ex + 12x + -6xy + -3x2 + -1ex + -2y = 0 + -1ex

Reorder the terms:
ex + -1ex + 12x + -6xy + -3x2 + -2y = 0 + -1ex

Combine like terms: ex + -1ex = 0
0 + 12x + -6xy + -3x2 + -2y = 0 + -1ex
12x + -6xy + -3x2 + -2y = 0 + -1ex
Remove the zero:
12x + -6xy + -3x2 + -2y = -1ex

Add '-12x' to each side of the equation.
12x + -6xy + -3x2 + -12x + -2y = -1ex + -12x

Reorder the terms:
12x + -12x + -6xy + -3x2 + -2y = -1ex + -12x

Combine like terms: 12x + -12x = 0
0 + -6xy + -3x2 + -2y = -1ex + -12x
-6xy + -3x2 + -2y = -1ex + -12x

Add '6xy' to each side of the equation.
-6xy + -3x2 + 6xy + -2y = -1ex + -12x + 6xy

Reorder the terms:
-6xy + 6xy + -3x2 + -2y = -1ex + -12x + 6xy

Combine like terms: -6xy + 6xy = 0
0 + -3x2 + -2y = -1ex + -12x + 6xy
-3x2 + -2y = -1ex + -12x + 6xy

Add '3x2' to each side of the equation.
-3x2 + 3x2 + -2y = -1ex + -12x + 6xy + 3x2

Combine like terms: -3x2 + 3x2 = 0
0 + -2y = -1ex + -12x + 6xy + 3x2
-2y = -1ex + -12x + 6xy + 3x2

Add '2y' to each side of the equation.
-2y + 2y = -1ex + -12x + 6xy + 3x2 + 2y

Combine like terms: -2y + 2y = 0
0 = -1ex + -12x + 6xy + 3x2 + 2y

Simplifying
0 = -1ex + -12x + 6xy + 3x2 + 2y

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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