(2x-6y+3)dx-(x-3y+1)dy=0

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Solution for (2x-6y+3)dx-(x-3y+1)dy=0 equation: 


Simplifying
(2x + -6y + 3) * dx + -1(x + -3y + 1) * dy = 0

Reorder the terms:
(3 + 2x + -6y) * dx + -1(x + -3y + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 2x + -6y) + -1(x + -3y + 1) * dy = 0
(3 * dx + 2x * dx + -6y * dx) + -1(x + -3y + 1) * dy = 0

Reorder the terms:
(3dx + -6dxy + 2dx2) + -1(x + -3y + 1) * dy = 0
(3dx + -6dxy + 2dx2) + -1(x + -3y + 1) * dy = 0

Reorder the terms:
3dx + -6dxy + 2dx2 + -1(1 + x + -3y) * dy = 0

Reorder the terms for easier multiplication:
3dx + -6dxy + 2dx2 + -1dy(1 + x + -3y) = 0
3dx + -6dxy + 2dx2 + (1 * -1dy + x * -1dy + -3y * -1dy) = 0

Reorder the terms:
3dx + -6dxy + 2dx2 + (-1dxy + -1dy + 3dy2) = 0
3dx + -6dxy + 2dx2 + (-1dxy + -1dy + 3dy2) = 0

Reorder the terms:
3dx + -6dxy + -1dxy + 2dx2 + -1dy + 3dy2 = 0

Combine like terms: -6dxy + -1dxy = -7dxy
3dx + -7dxy + 2dx2 + -1dy + 3dy2 = 0

Solving
3dx + -7dxy + 2dx2 + -1dy + 3dy2 = 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 + -7xy + 2x2 + -1y + 3y2) = 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 + -7xy + 2x2 + -1y + 3y2)' equal to zero and attempt to solve:

Simplifying
3x + -7xy + 2x2 + -1y + 3y2 = 0

Solving
3x + -7xy + 2x2 + -1y + 3y2 = 0

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

Add '-3x' to each side of the equation.
3x + -7xy + 2x2 + -1y + -3x + 3y2 = 0 + -3x

Reorder the terms:
3x + -3x + -7xy + 2x2 + -1y + 3y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + -7xy + 2x2 + -1y + 3y2 = 0 + -3x
-7xy + 2x2 + -1y + 3y2 = 0 + -3x
Remove the zero:
-7xy + 2x2 + -1y + 3y2 = -3x

Add '7xy' to each side of the equation.
-7xy + 2x2 + -1y + 7xy + 3y2 = -3x + 7xy

Reorder the terms:
-7xy + 7xy + 2x2 + -1y + 3y2 = -3x + 7xy

Combine like terms: -7xy + 7xy = 0
0 + 2x2 + -1y + 3y2 = -3x + 7xy
2x2 + -1y + 3y2 = -3x + 7xy

Add '-2x2' to each side of the equation.
2x2 + -1y + -2x2 + 3y2 = -3x + 7xy + -2x2

Reorder the terms:
2x2 + -2x2 + -1y + 3y2 = -3x + 7xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y + 3y2 = -3x + 7xy + -2x2
-1y + 3y2 = -3x + 7xy + -2x2

Add 'y' to each side of the equation.
-1y + y + 3y2 = -3x + 7xy + -2x2 + y

Combine like terms: -1y + y = 0
0 + 3y2 = -3x + 7xy + -2x2 + y
3y2 = -3x + 7xy + -2x2 + y

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -3x + 7xy + -2x2 + y + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -3x + 7xy + -2x2 + y + -3y2

Simplifying
0 = -3x + 7xy + -2x2 + y + -3y2

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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