(x+y)dx+(6x+6y-1)dy=0

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Solution for (x+y)dx+(6x+6y-1)dy=0 equation: 


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

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

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

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

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

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

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

Combine like terms: dxy + 6dxy = 7dxy
7dxy + dx2 + -1dy + 6dy2 = 0

Solving
7dxy + dx2 + -1dy + 6dy2 = 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(7xy + x2 + -1y + 6y2) = 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 '(7xy + x2 + -1y + 6y2)' equal to zero and attempt to solve:

Simplifying
7xy + x2 + -1y + 6y2 = 0

Solving
7xy + x2 + -1y + 6y2 = 0

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

Add '-7xy' to each side of the equation.
7xy + x2 + -1y + -7xy + 6y2 = 0 + -7xy

Reorder the terms:
7xy + -7xy + x2 + -1y + 6y2 = 0 + -7xy

Combine like terms: 7xy + -7xy = 0
0 + x2 + -1y + 6y2 = 0 + -7xy
x2 + -1y + 6y2 = 0 + -7xy
Remove the zero:
x2 + -1y + 6y2 = -7xy

Add '-1x2' to each side of the equation.
x2 + -1y + -1x2 + 6y2 = -7xy + -1x2

Reorder the terms:
x2 + -1x2 + -1y + 6y2 = -7xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1y + 6y2 = -7xy + -1x2
-1y + 6y2 = -7xy + -1x2

Add 'y' to each side of the equation.
-1y + y + 6y2 = -7xy + -1x2 + y

Combine like terms: -1y + y = 0
0 + 6y2 = -7xy + -1x2 + y
6y2 = -7xy + -1x2 + y

Add '-6y2' to each side of the equation.
6y2 + -6y2 = -7xy + -1x2 + y + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = -7xy + -1x2 + y + -6y2

Simplifying
0 = -7xy + -1x2 + y + -6y2

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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