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

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


Simplifying
(2x + y + 4) * dx + -1(2x + y + -6) * dy = 0

Reorder the terms:
(4 + 2x + y) * dx + -1(2x + y + -6) * dy = 0

Reorder the terms for easier multiplication:
dx(4 + 2x + y) + -1(2x + y + -6) * dy = 0
(4 * dx + 2x * dx + y * dx) + -1(2x + y + -6) * dy = 0

Reorder the terms:
(4dx + dxy + 2dx2) + -1(2x + y + -6) * dy = 0
(4dx + dxy + 2dx2) + -1(2x + y + -6) * dy = 0

Reorder the terms:
4dx + dxy + 2dx2 + -1(-6 + 2x + y) * dy = 0

Reorder the terms for easier multiplication:
4dx + dxy + 2dx2 + -1dy(-6 + 2x + y) = 0
4dx + dxy + 2dx2 + (-6 * -1dy + 2x * -1dy + y * -1dy) = 0

Reorder the terms:
4dx + dxy + 2dx2 + (-2dxy + 6dy + -1dy2) = 0
4dx + dxy + 2dx2 + (-2dxy + 6dy + -1dy2) = 0

Reorder the terms:
4dx + dxy + -2dxy + 2dx2 + 6dy + -1dy2 = 0

Combine like terms: dxy + -2dxy = -1dxy
4dx + -1dxy + 2dx2 + 6dy + -1dy2 = 0

Solving
4dx + -1dxy + 2dx2 + 6dy + -1dy2 = 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 + -1xy + 2x2 + 6y + -1y2) = 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 + -1xy + 2x2 + 6y + -1y2)' equal to zero and attempt to solve:

Simplifying
4x + -1xy + 2x2 + 6y + -1y2 = 0

Solving
4x + -1xy + 2x2 + 6y + -1y2 = 0

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

Add '-4x' to each side of the equation.
4x + -1xy + 2x2 + 6y + -4x + -1y2 = 0 + -4x

Reorder the terms:
4x + -4x + -1xy + 2x2 + 6y + -1y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + -1xy + 2x2 + 6y + -1y2 = 0 + -4x
-1xy + 2x2 + 6y + -1y2 = 0 + -4x
Remove the zero:
-1xy + 2x2 + 6y + -1y2 = -4x

Add 'xy' to each side of the equation.
-1xy + 2x2 + 6y + xy + -1y2 = -4x + xy

Reorder the terms:
-1xy + xy + 2x2 + 6y + -1y2 = -4x + xy

Combine like terms: -1xy + xy = 0
0 + 2x2 + 6y + -1y2 = -4x + xy
2x2 + 6y + -1y2 = -4x + xy

Add '-2x2' to each side of the equation.
2x2 + 6y + -2x2 + -1y2 = -4x + xy + -2x2

Reorder the terms:
2x2 + -2x2 + 6y + -1y2 = -4x + xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 6y + -1y2 = -4x + xy + -2x2
6y + -1y2 = -4x + xy + -2x2

Add '-6y' to each side of the equation.
6y + -6y + -1y2 = -4x + xy + -2x2 + -6y

Combine like terms: 6y + -6y = 0
0 + -1y2 = -4x + xy + -2x2 + -6y
-1y2 = -4x + xy + -2x2 + -6y

Add 'y2' to each side of the equation.
-1y2 + y2 = -4x + xy + -2x2 + -6y + y2

Combine like terms: -1y2 + y2 = 0
0 = -4x + xy + -2x2 + -6y + y2

Simplifying
0 = -4x + xy + -2x2 + -6y + y2

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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