(6x+y^2)dx+(2x-3y)dy=0

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Solution for (6x+y^2)dx+(2x-3y)dy=0 equation: 


Simplifying
(6x + y2) * dx + (2x + -3y) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + y2) + (2x + -3y) * dy = 0
(6x * dx + y2 * dx) + (2x + -3y) * dy = 0

Reorder the terms:
(dxy2 + 6dx2) + (2x + -3y) * dy = 0
(dxy2 + 6dx2) + (2x + -3y) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx2 + dy(2x + -3y) = 0
dxy2 + 6dx2 + (2x * dy + -3y * dy) = 0
dxy2 + 6dx2 + (2dxy + -3dy2) = 0

Reorder the terms:
2dxy + dxy2 + 6dx2 + -3dy2 = 0

Solving
2dxy + dxy2 + 6dx2 + -3dy2 = 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(2xy + xy2 + 6x2 + -3y2) = 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 '(2xy + xy2 + 6x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
2xy + xy2 + 6x2 + -3y2 = 0

Solving
2xy + xy2 + 6x2 + -3y2 = 0

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

Add '-2xy' to each side of the equation.
2xy + xy2 + 6x2 + -2xy + -3y2 = 0 + -2xy

Reorder the terms:
2xy + -2xy + xy2 + 6x2 + -3y2 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + xy2 + 6x2 + -3y2 = 0 + -2xy
xy2 + 6x2 + -3y2 = 0 + -2xy
Remove the zero:
xy2 + 6x2 + -3y2 = -2xy

Add '-1xy2' to each side of the equation.
xy2 + 6x2 + -1xy2 + -3y2 = -2xy + -1xy2

Reorder the terms:
xy2 + -1xy2 + 6x2 + -3y2 = -2xy + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + 6x2 + -3y2 = -2xy + -1xy2
6x2 + -3y2 = -2xy + -1xy2

Add '-6x2' to each side of the equation.
6x2 + -6x2 + -3y2 = -2xy + -1xy2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + -3y2 = -2xy + -1xy2 + -6x2
-3y2 = -2xy + -1xy2 + -6x2

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -2xy + -1xy2 + -6x2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -2xy + -1xy2 + -6x2 + 3y2

Simplifying
0 = -2xy + -1xy2 + -6x2 + 3y2

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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