(x+2y-1)dx-(x+2y-5)dy=0

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Solution for (x+2y-1)dx-(x+2y-5)dy=0 equation: 


Simplifying
(x + 2y + -1) * dx + -1(x + 2y + -5) * dy = 0

Reorder the terms:
(-1 + x + 2y) * dx + -1(x + 2y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + x + 2y) + -1(x + 2y + -5) * dy = 0
(-1 * dx + x * dx + 2y * dx) + -1(x + 2y + -5) * dy = 0

Reorder the terms:
(-1dx + 2dxy + dx2) + -1(x + 2y + -5) * dy = 0
(-1dx + 2dxy + dx2) + -1(x + 2y + -5) * dy = 0

Reorder the terms:
-1dx + 2dxy + dx2 + -1(-5 + x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 2dxy + dx2 + -1dy(-5 + x + 2y) = 0
-1dx + 2dxy + dx2 + (-5 * -1dy + x * -1dy + 2y * -1dy) = 0

Reorder the terms:
-1dx + 2dxy + dx2 + (-1dxy + 5dy + -2dy2) = 0
-1dx + 2dxy + dx2 + (-1dxy + 5dy + -2dy2) = 0

Reorder the terms:
-1dx + 2dxy + -1dxy + dx2 + 5dy + -2dy2 = 0

Combine like terms: 2dxy + -1dxy = 1dxy
-1dx + 1dxy + dx2 + 5dy + -2dy2 = 0

Solving
-1dx + 1dxy + dx2 + 5dy + -2dy2 = 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 + xy + x2 + 5y + -2y2) = 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 + xy + x2 + 5y + -2y2)' equal to zero and attempt to solve:

Simplifying
-1x + xy + x2 + 5y + -2y2 = 0

Solving
-1x + xy + x2 + 5y + -2y2 = 0

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

Add 'x' to each side of the equation.
-1x + xy + x2 + 5y + x + -2y2 = 0 + x

Reorder the terms:
-1x + x + xy + x2 + 5y + -2y2 = 0 + x

Combine like terms: -1x + x = 0
0 + xy + x2 + 5y + -2y2 = 0 + x
xy + x2 + 5y + -2y2 = 0 + x
Remove the zero:
xy + x2 + 5y + -2y2 = x

Add '-1xy' to each side of the equation.
xy + x2 + 5y + -1xy + -2y2 = x + -1xy

Reorder the terms:
xy + -1xy + x2 + 5y + -2y2 = x + -1xy

Combine like terms: xy + -1xy = 0
0 + x2 + 5y + -2y2 = x + -1xy
x2 + 5y + -2y2 = x + -1xy

Add '-1x2' to each side of the equation.
x2 + 5y + -1x2 + -2y2 = x + -1xy + -1x2

Reorder the terms:
x2 + -1x2 + 5y + -2y2 = x + -1xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 5y + -2y2 = x + -1xy + -1x2
5y + -2y2 = x + -1xy + -1x2

Add '-5y' to each side of the equation.
5y + -5y + -2y2 = x + -1xy + -1x2 + -5y

Combine like terms: 5y + -5y = 0
0 + -2y2 = x + -1xy + -1x2 + -5y
-2y2 = x + -1xy + -1x2 + -5y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = x + -1xy + -1x2 + -5y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = x + -1xy + -1x2 + -5y + 2y2

Simplifying
0 = x + -1xy + -1x2 + -5y + 2y2

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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