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

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


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

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

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

Reorder the terms:
(2dx + -3dxy + dx2) + 3(x + 3y + -4) * dy = 0
(2dx + -3dxy + dx2) + 3(x + 3y + -4) * dy = 0

Reorder the terms:
2dx + -3dxy + dx2 + 3(-4 + x + 3y) * dy = 0

Reorder the terms for easier multiplication:
2dx + -3dxy + dx2 + 3dy(-4 + x + 3y) = 0
2dx + -3dxy + dx2 + (-4 * 3dy + x * 3dy + 3y * 3dy) = 0

Reorder the terms:
2dx + -3dxy + dx2 + (3dxy + -12dy + 9dy2) = 0
2dx + -3dxy + dx2 + (3dxy + -12dy + 9dy2) = 0

Reorder the terms:
2dx + -3dxy + 3dxy + dx2 + -12dy + 9dy2 = 0

Combine like terms: -3dxy + 3dxy = 0
2dx + 0 + dx2 + -12dy + 9dy2 = 0
2dx + dx2 + -12dy + 9dy2 = 0

Solving
2dx + dx2 + -12dy + 9dy2 = 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(2x + x2 + -12y + 9y2) = 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 '(2x + x2 + -12y + 9y2)' equal to zero and attempt to solve:

Simplifying
2x + x2 + -12y + 9y2 = 0

Solving
2x + x2 + -12y + 9y2 = 0

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

Add '-2x' to each side of the equation.
2x + x2 + -12y + -2x + 9y2 = 0 + -2x

Reorder the terms:
2x + -2x + x2 + -12y + 9y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + x2 + -12y + 9y2 = 0 + -2x
x2 + -12y + 9y2 = 0 + -2x
Remove the zero:
x2 + -12y + 9y2 = -2x

Add '-1x2' to each side of the equation.
x2 + -12y + -1x2 + 9y2 = -2x + -1x2

Reorder the terms:
x2 + -1x2 + -12y + 9y2 = -2x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -12y + 9y2 = -2x + -1x2
-12y + 9y2 = -2x + -1x2

Add '12y' to each side of the equation.
-12y + 12y + 9y2 = -2x + -1x2 + 12y

Combine like terms: -12y + 12y = 0
0 + 9y2 = -2x + -1x2 + 12y
9y2 = -2x + -1x2 + 12y

Add '-9y2' to each side of the equation.
9y2 + -9y2 = -2x + -1x2 + 12y + -9y2

Combine like terms: 9y2 + -9y2 = 0
0 = -2x + -1x2 + 12y + -9y2

Simplifying
0 = -2x + -1x2 + 12y + -9y2

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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