(1x-3y+3)dx+(3x+y+9)dy=0

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Solution for (1x-3y+3)dx+(3x+y+9)dy=0 equation: 


Simplifying
(1x + -3y + 3) * dx + (3x + y + 9) * dy = 0

Reorder the terms:
(3 + 1x + -3y) * dx + (3x + y + 9) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 1x + -3y) + (3x + y + 9) * dy = 0
(3 * dx + 1x * dx + -3y * dx) + (3x + y + 9) * dy = 0

Reorder the terms:
(3dx + -3dxy + 1dx2) + (3x + y + 9) * dy = 0
(3dx + -3dxy + 1dx2) + (3x + y + 9) * dy = 0

Reorder the terms:
3dx + -3dxy + 1dx2 + (9 + 3x + y) * dy = 0

Reorder the terms for easier multiplication:
3dx + -3dxy + 1dx2 + dy(9 + 3x + y) = 0
3dx + -3dxy + 1dx2 + (9 * dy + 3x * dy + y * dy) = 0

Reorder the terms:
3dx + -3dxy + 1dx2 + (3dxy + 9dy + dy2) = 0
3dx + -3dxy + 1dx2 + (3dxy + 9dy + dy2) = 0

Reorder the terms:
3dx + -3dxy + 3dxy + 1dx2 + 9dy + dy2 = 0

Combine like terms: -3dxy + 3dxy = 0
3dx + 0 + 1dx2 + 9dy + dy2 = 0
3dx + 1dx2 + 9dy + dy2 = 0

Solving
3dx + 1dx2 + 9dy + dy2 = 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 + x2 + 9y + y2) = 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 + x2 + 9y + y2)' equal to zero and attempt to solve:

Simplifying
3x + x2 + 9y + y2 = 0

Solving
3x + x2 + 9y + y2 = 0

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

Add '-3x' to each side of the equation.
3x + x2 + 9y + -3x + y2 = 0 + -3x

Reorder the terms:
3x + -3x + x2 + 9y + y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + x2 + 9y + y2 = 0 + -3x
x2 + 9y + y2 = 0 + -3x
Remove the zero:
x2 + 9y + y2 = -3x

Add '-1x2' to each side of the equation.
x2 + 9y + -1x2 + y2 = -3x + -1x2

Reorder the terms:
x2 + -1x2 + 9y + y2 = -3x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 9y + y2 = -3x + -1x2
9y + y2 = -3x + -1x2

Add '-9y' to each side of the equation.
9y + -9y + y2 = -3x + -1x2 + -9y

Combine like terms: 9y + -9y = 0
0 + y2 = -3x + -1x2 + -9y
y2 = -3x + -1x2 + -9y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3x + -1x2 + -9y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3x + -1x2 + -9y + -1y2

Simplifying
0 = -3x + -1x2 + -9y + -1y2

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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