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

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


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

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

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

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

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

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

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

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

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

Solving
4dx + dx2 + -6dy + -4dy2 = 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(4x + x2 + -6y + -4y2) = 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 '(4x + x2 + -6y + -4y2)' equal to zero and attempt to solve:

Simplifying
4x + x2 + -6y + -4y2 = 0

Solving
4x + x2 + -6y + -4y2 = 0

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

Add '-4x' to each side of the equation.
4x + x2 + -6y + -4x + -4y2 = 0 + -4x

Reorder the terms:
4x + -4x + x2 + -6y + -4y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + x2 + -6y + -4y2 = 0 + -4x
x2 + -6y + -4y2 = 0 + -4x
Remove the zero:
x2 + -6y + -4y2 = -4x

Add '-1x2' to each side of the equation.
x2 + -6y + -1x2 + -4y2 = -4x + -1x2

Reorder the terms:
x2 + -1x2 + -6y + -4y2 = -4x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -6y + -4y2 = -4x + -1x2
-6y + -4y2 = -4x + -1x2

Add '6y' to each side of the equation.
-6y + 6y + -4y2 = -4x + -1x2 + 6y

Combine like terms: -6y + 6y = 0
0 + -4y2 = -4x + -1x2 + 6y
-4y2 = -4x + -1x2 + 6y

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -4x + -1x2 + 6y + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -4x + -1x2 + 6y + 4y2

Simplifying
0 = -4x + -1x2 + 6y + 4y2

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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