(2x+y-1)dx-(4x+2y+5)dy=0

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Solution for (2x+y-1)dx-(4x+2y+5)dy=0 equation: 


Simplifying
(2x + y + -1) * dx + -1(4x + 2y + 5) * dy = 0

Reorder the terms:
(-1 + 2x + y) * dx + -1(4x + 2y + 5) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2x + y) + -1(4x + 2y + 5) * dy = 0
(-1 * dx + 2x * dx + y * dx) + -1(4x + 2y + 5) * dy = 0

Reorder the terms:
(-1dx + dxy + 2dx2) + -1(4x + 2y + 5) * dy = 0
(-1dx + dxy + 2dx2) + -1(4x + 2y + 5) * dy = 0

Reorder the terms:
-1dx + dxy + 2dx2 + -1(5 + 4x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + dxy + 2dx2 + -1dy(5 + 4x + 2y) = 0
-1dx + dxy + 2dx2 + (5 * -1dy + 4x * -1dy + 2y * -1dy) = 0

Reorder the terms:
-1dx + dxy + 2dx2 + (-4dxy + -5dy + -2dy2) = 0
-1dx + dxy + 2dx2 + (-4dxy + -5dy + -2dy2) = 0

Reorder the terms:
-1dx + dxy + -4dxy + 2dx2 + -5dy + -2dy2 = 0

Combine like terms: dxy + -4dxy = -3dxy
-1dx + -3dxy + 2dx2 + -5dy + -2dy2 = 0

Solving
-1dx + -3dxy + 2dx2 + -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 + -3xy + 2x2 + -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 + -3xy + 2x2 + -5y + -2y2)' equal to zero and attempt to solve:

Simplifying
-1x + -3xy + 2x2 + -5y + -2y2 = 0

Solving
-1x + -3xy + 2x2 + -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 + -3xy + 2x2 + -5y + x + -2y2 = 0 + x

Reorder the terms:
-1x + x + -3xy + 2x2 + -5y + -2y2 = 0 + x

Combine like terms: -1x + x = 0
0 + -3xy + 2x2 + -5y + -2y2 = 0 + x
-3xy + 2x2 + -5y + -2y2 = 0 + x
Remove the zero:
-3xy + 2x2 + -5y + -2y2 = x

Add '3xy' to each side of the equation.
-3xy + 2x2 + -5y + 3xy + -2y2 = x + 3xy

Reorder the terms:
-3xy + 3xy + 2x2 + -5y + -2y2 = x + 3xy

Combine like terms: -3xy + 3xy = 0
0 + 2x2 + -5y + -2y2 = x + 3xy
2x2 + -5y + -2y2 = x + 3xy

Add '-2x2' to each side of the equation.
2x2 + -5y + -2x2 + -2y2 = x + 3xy + -2x2

Reorder the terms:
2x2 + -2x2 + -5y + -2y2 = x + 3xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -5y + -2y2 = x + 3xy + -2x2
-5y + -2y2 = x + 3xy + -2x2

Add '5y' to each side of the equation.
-5y + 5y + -2y2 = x + 3xy + -2x2 + 5y

Combine like terms: -5y + 5y = 0
0 + -2y2 = x + 3xy + -2x2 + 5y
-2y2 = x + 3xy + -2x2 + 5y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = x + 3xy + -2x2 + 5y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = x + 3xy + -2x2 + 5y + 2y2

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