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

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


Simplifying
(x2 + 6xy + -3y2) * dx + (2xy + -3y2) * dy = 0

Reorder the terms:
(6xy + x2 + -3y2) * dx + (2xy + -3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(6xy + x2 + -3y2) + (2xy + -3y2) * dy = 0
(6xy * dx + x2 * dx + -3y2 * dx) + (2xy + -3y2) * dy = 0

Reorder the terms:
(-3dxy2 + 6dx2y + dx3) + (2xy + -3y2) * dy = 0
(-3dxy2 + 6dx2y + dx3) + (2xy + -3y2) * dy = 0

Reorder the terms for easier multiplication:
-3dxy2 + 6dx2y + dx3 + dy(2xy + -3y2) = 0
-3dxy2 + 6dx2y + dx3 + (2xy * dy + -3y2 * dy) = 0
-3dxy2 + 6dx2y + dx3 + (2dxy2 + -3dy3) = 0

Reorder the terms:
-3dxy2 + 2dxy2 + 6dx2y + dx3 + -3dy3 = 0

Combine like terms: -3dxy2 + 2dxy2 = -1dxy2
-1dxy2 + 6dx2y + dx3 + -3dy3 = 0

Solving
-1dxy2 + 6dx2y + dx3 + -3dy3 = 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(-1xy2 + 6x2y + x3 + -3y3) = 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 '(-1xy2 + 6x2y + x3 + -3y3)' equal to zero and attempt to solve:

Simplifying
-1xy2 + 6x2y + x3 + -3y3 = 0

Solving
-1xy2 + 6x2y + x3 + -3y3 = 0

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

Add 'xy2' to each side of the equation.
-1xy2 + 6x2y + x3 + xy2 + -3y3 = 0 + xy2

Reorder the terms:
-1xy2 + xy2 + 6x2y + x3 + -3y3 = 0 + xy2

Combine like terms: -1xy2 + xy2 = 0
0 + 6x2y + x3 + -3y3 = 0 + xy2
6x2y + x3 + -3y3 = 0 + xy2
Remove the zero:
6x2y + x3 + -3y3 = xy2

Add '-6x2y' to each side of the equation.
6x2y + x3 + -6x2y + -3y3 = xy2 + -6x2y

Reorder the terms:
6x2y + -6x2y + x3 + -3y3 = xy2 + -6x2y

Combine like terms: 6x2y + -6x2y = 0
0 + x3 + -3y3 = xy2 + -6x2y
x3 + -3y3 = xy2 + -6x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + -3y3 = xy2 + -6x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -3y3 = xy2 + -6x2y + -1x3
-3y3 = xy2 + -6x2y + -1x3

Add '3y3' to each side of the equation.
-3y3 + 3y3 = xy2 + -6x2y + -1x3 + 3y3

Combine like terms: -3y3 + 3y3 = 0
0 = xy2 + -6x2y + -1x3 + 3y3

Simplifying
0 = xy2 + -6x2y + -1x3 + 3y3

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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