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

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


Simplifying
(6x + y2d) * dy + y(2x + -3y) * dy = 0

Reorder the terms:
(dy2 + 6x) * dy + y(2x + -3y) * dy = 0

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

Reorder the terms:
(6dxy + d2y3) + y(2x + -3y) * dy = 0
(6dxy + d2y3) + y(2x + -3y) * dy = 0

Reorder the terms for easier multiplication:
6dxy + d2y3 + y * dy(2x + -3y) = 0

Multiply y * dy
6dxy + d2y3 + dy2(2x + -3y) = 0
6dxy + d2y3 + (2x * dy2 + -3y * dy2) = 0
6dxy + d2y3 + (2dxy2 + -3dy3) = 0

Reorder the terms:
6dxy + 2dxy2 + -3dy3 + d2y3 = 0

Solving
6dxy + 2dxy2 + -3dy3 + d2y3 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(6x + 2xy + -3y2 + dy2) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(6x + 2xy + -3y2 + dy2)' equal to zero and attempt to solve:

Simplifying
6x + 2xy + -3y2 + dy2 = 0

Reorder the terms:
dy2 + 6x + 2xy + -3y2 = 0

Solving
dy2 + 6x + 2xy + -3y2 = 0

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

Add '-6x' to each side of the equation.
dy2 + 6x + 2xy + -6x + -3y2 = 0 + -6x

Reorder the terms:
dy2 + 6x + -6x + 2xy + -3y2 = 0 + -6x

Combine like terms: 6x + -6x = 0
dy2 + 0 + 2xy + -3y2 = 0 + -6x
dy2 + 2xy + -3y2 = 0 + -6x
Remove the zero:
dy2 + 2xy + -3y2 = -6x

Add '-2xy' to each side of the equation.
dy2 + 2xy + -2xy + -3y2 = -6x + -2xy

Combine like terms: 2xy + -2xy = 0
dy2 + 0 + -3y2 = -6x + -2xy
dy2 + -3y2 = -6x + -2xy

Add '3y2' to each side of the equation.
dy2 + -3y2 + 3y2 = -6x + -2xy + 3y2

Combine like terms: -3y2 + 3y2 = 0
dy2 + 0 = -6x + -2xy + 3y2
dy2 = -6x + -2xy + 3y2

Divide each side by 'y2'.
d = -6xy-2 + -2xy-1 + 3

Simplifying
d = -6xy-2 + -2xy-1 + 3

Reorder the terms:
d = 3 + -6xy-2 + -2xy-1
Solution
d = {3 + -6xy-2 + -2xy-1}

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