(x+2y-1)dx+(2x+4y-3)dy=0

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Solution for (x+2y-1)dx+(2x+4y-3)dy=0 equation: 


Simplifying
(x + 2y + -1) * dx + (2x + 4y + -3) * dy = 0

Reorder the terms:
(-1 + x + 2y) * dx + (2x + 4y + -3) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + x + 2y) + (2x + 4y + -3) * dy = 0
(-1 * dx + x * dx + 2y * dx) + (2x + 4y + -3) * dy = 0

Reorder the terms:
(-1dx + 2dxy + dx2) + (2x + 4y + -3) * dy = 0
(-1dx + 2dxy + dx2) + (2x + 4y + -3) * dy = 0

Reorder the terms:
-1dx + 2dxy + dx2 + (-3 + 2x + 4y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 2dxy + dx2 + dy(-3 + 2x + 4y) = 0
-1dx + 2dxy + dx2 + (-3 * dy + 2x * dy + 4y * dy) = 0

Reorder the terms:
-1dx + 2dxy + dx2 + (2dxy + -3dy + 4dy2) = 0
-1dx + 2dxy + dx2 + (2dxy + -3dy + 4dy2) = 0

Reorder the terms:
-1dx + 2dxy + 2dxy + dx2 + -3dy + 4dy2 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
-1dx + 4dxy + dx2 + -3dy + 4dy2 = 0

Solving
-1dx + 4dxy + dx2 + -3dy + 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(-1x + 4xy + x2 + -3y + 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 '(-1x + 4xy + x2 + -3y + 4y2)' equal to zero and attempt to solve:

Simplifying
-1x + 4xy + x2 + -3y + 4y2 = 0

Solving
-1x + 4xy + x2 + -3y + 4y2 = 0

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

Add 'x' to each side of the equation.
-1x + 4xy + x2 + -3y + x + 4y2 = 0 + x

Reorder the terms:
-1x + x + 4xy + x2 + -3y + 4y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 4xy + x2 + -3y + 4y2 = 0 + x
4xy + x2 + -3y + 4y2 = 0 + x
Remove the zero:
4xy + x2 + -3y + 4y2 = x

Add '-4xy' to each side of the equation.
4xy + x2 + -3y + -4xy + 4y2 = x + -4xy

Reorder the terms:
4xy + -4xy + x2 + -3y + 4y2 = x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + x2 + -3y + 4y2 = x + -4xy
x2 + -3y + 4y2 = x + -4xy

Add '-1x2' to each side of the equation.
x2 + -3y + -1x2 + 4y2 = x + -4xy + -1x2

Reorder the terms:
x2 + -1x2 + -3y + 4y2 = x + -4xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -3y + 4y2 = x + -4xy + -1x2
-3y + 4y2 = x + -4xy + -1x2

Add '3y' to each side of the equation.
-3y + 3y + 4y2 = x + -4xy + -1x2 + 3y

Combine like terms: -3y + 3y = 0
0 + 4y2 = x + -4xy + -1x2 + 3y
4y2 = x + -4xy + -1x2 + 3y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = x + -4xy + -1x2 + 3y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = x + -4xy + -1x2 + 3y + -4y2

Simplifying
0 = x + -4xy + -1x2 + 3y + -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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