(12x+4y-8)dx-(3x+y)dy=0

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Solution for (12x+4y-8)dx-(3x+y)dy=0 equation: 


Simplifying
(12x + 4y + -8) * dx + -1(3x + y) * dy = 0

Reorder the terms:
(-8 + 12x + 4y) * dx + -1(3x + y) * dy = 0

Reorder the terms for easier multiplication:
dx(-8 + 12x + 4y) + -1(3x + y) * dy = 0
(-8 * dx + 12x * dx + 4y * dx) + -1(3x + y) * dy = 0

Reorder the terms:
(-8dx + 4dxy + 12dx2) + -1(3x + y) * dy = 0
(-8dx + 4dxy + 12dx2) + -1(3x + y) * dy = 0

Reorder the terms for easier multiplication:
-8dx + 4dxy + 12dx2 + -1dy(3x + y) = 0
-8dx + 4dxy + 12dx2 + (3x * -1dy + y * -1dy) = 0
-8dx + 4dxy + 12dx2 + (-3dxy + -1dy2) = 0

Reorder the terms:
-8dx + 4dxy + -3dxy + 12dx2 + -1dy2 = 0

Combine like terms: 4dxy + -3dxy = 1dxy
-8dx + 1dxy + 12dx2 + -1dy2 = 0

Solving
-8dx + 1dxy + 12dx2 + -1dy2 = 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(-8x + xy + 12x2 + -1y2) = 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 '(-8x + xy + 12x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
-8x + xy + 12x2 + -1y2 = 0

Solving
-8x + xy + 12x2 + -1y2 = 0

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

Add '8x' to each side of the equation.
-8x + xy + 12x2 + 8x + -1y2 = 0 + 8x

Reorder the terms:
-8x + 8x + xy + 12x2 + -1y2 = 0 + 8x

Combine like terms: -8x + 8x = 0
0 + xy + 12x2 + -1y2 = 0 + 8x
xy + 12x2 + -1y2 = 0 + 8x
Remove the zero:
xy + 12x2 + -1y2 = 8x

Add '-1xy' to each side of the equation.
xy + 12x2 + -1xy + -1y2 = 8x + -1xy

Reorder the terms:
xy + -1xy + 12x2 + -1y2 = 8x + -1xy

Combine like terms: xy + -1xy = 0
0 + 12x2 + -1y2 = 8x + -1xy
12x2 + -1y2 = 8x + -1xy

Add '-12x2' to each side of the equation.
12x2 + -12x2 + -1y2 = 8x + -1xy + -12x2

Combine like terms: 12x2 + -12x2 = 0
0 + -1y2 = 8x + -1xy + -12x2
-1y2 = 8x + -1xy + -12x2

Add 'y2' to each side of the equation.
-1y2 + y2 = 8x + -1xy + -12x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = 8x + -1xy + -12x2 + y2

Simplifying
0 = 8x + -1xy + -12x2 + y2

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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