(2x-4y+6)dx+(x+y-3)dy=0

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Solution for (2x-4y+6)dx+(x+y-3)dy=0 equation: 


Simplifying
(2x + -4y + 6) * dx + (x + y + -3) * dy = 0

Reorder the terms:
(6 + 2x + -4y) * dx + (x + y + -3) * dy = 0

Reorder the terms for easier multiplication:
dx(6 + 2x + -4y) + (x + y + -3) * dy = 0
(6 * dx + 2x * dx + -4y * dx) + (x + y + -3) * dy = 0

Reorder the terms:
(6dx + -4dxy + 2dx2) + (x + y + -3) * dy = 0
(6dx + -4dxy + 2dx2) + (x + y + -3) * dy = 0

Reorder the terms:
6dx + -4dxy + 2dx2 + (-3 + x + y) * dy = 0

Reorder the terms for easier multiplication:
6dx + -4dxy + 2dx2 + dy(-3 + x + y) = 0
6dx + -4dxy + 2dx2 + (-3 * dy + x * dy + y * dy) = 0

Reorder the terms:
6dx + -4dxy + 2dx2 + (dxy + -3dy + dy2) = 0
6dx + -4dxy + 2dx2 + (dxy + -3dy + dy2) = 0

Reorder the terms:
6dx + -4dxy + dxy + 2dx2 + -3dy + dy2 = 0

Combine like terms: -4dxy + dxy = -3dxy
6dx + -3dxy + 2dx2 + -3dy + dy2 = 0

Solving
6dx + -3dxy + 2dx2 + -3dy + 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(6x + -3xy + 2x2 + -3y + 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 '(6x + -3xy + 2x2 + -3y + y2)' equal to zero and attempt to solve:

Simplifying
6x + -3xy + 2x2 + -3y + y2 = 0

Solving
6x + -3xy + 2x2 + -3y + y2 = 0

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

Add '-6x' to each side of the equation.
6x + -3xy + 2x2 + -3y + -6x + y2 = 0 + -6x

Reorder the terms:
6x + -6x + -3xy + 2x2 + -3y + y2 = 0 + -6x

Combine like terms: 6x + -6x = 0
0 + -3xy + 2x2 + -3y + y2 = 0 + -6x
-3xy + 2x2 + -3y + y2 = 0 + -6x
Remove the zero:
-3xy + 2x2 + -3y + y2 = -6x

Add '3xy' to each side of the equation.
-3xy + 2x2 + -3y + 3xy + y2 = -6x + 3xy

Reorder the terms:
-3xy + 3xy + 2x2 + -3y + y2 = -6x + 3xy

Combine like terms: -3xy + 3xy = 0
0 + 2x2 + -3y + y2 = -6x + 3xy
2x2 + -3y + y2 = -6x + 3xy

Add '-2x2' to each side of the equation.
2x2 + -3y + -2x2 + y2 = -6x + 3xy + -2x2

Reorder the terms:
2x2 + -2x2 + -3y + y2 = -6x + 3xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -3y + y2 = -6x + 3xy + -2x2
-3y + y2 = -6x + 3xy + -2x2

Add '3y' to each side of the equation.
-3y + 3y + y2 = -6x + 3xy + -2x2 + 3y

Combine like terms: -3y + 3y = 0
0 + y2 = -6x + 3xy + -2x2 + 3y
y2 = -6x + 3xy + -2x2 + 3y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -6x + 3xy + -2x2 + 3y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -6x + 3xy + -2x2 + 3y + -1y2

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