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

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


Simplifying
(y2 + -3y + -1x) * dx + (2y + -3) * dy = 0

Reorder the terms:
(-1x + -3y + y2) * dx + (2y + -3) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x + -3y + y2) + (2y + -3) * dy = 0
(-1x * dx + -3y * dx + y2 * dx) + (2y + -3) * dy = 0

Reorder the terms:
(-3dxy + dxy2 + -1dx2) + (2y + -3) * dy = 0
(-3dxy + dxy2 + -1dx2) + (2y + -3) * dy = 0

Reorder the terms:
-3dxy + dxy2 + -1dx2 + (-3 + 2y) * dy = 0

Reorder the terms for easier multiplication:
-3dxy + dxy2 + -1dx2 + dy(-3 + 2y) = 0
-3dxy + dxy2 + -1dx2 + (-3 * dy + 2y * dy) = 0
-3dxy + dxy2 + -1dx2 + (-3dy + 2dy2) = 0

Solving
-3dxy + dxy2 + -1dx2 + -3dy + 2dy2 = 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(-3xy + xy2 + -1x2 + -3y + 2y2) = 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 '(-3xy + xy2 + -1x2 + -3y + 2y2)' equal to zero and attempt to solve:

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

Solving
-3xy + xy2 + -1x2 + -3y + 2y2 = 0

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

Add '3xy' to each side of the equation.
-3xy + xy2 + -1x2 + -3y + 3xy + 2y2 = 0 + 3xy

Reorder the terms:
-3xy + 3xy + xy2 + -1x2 + -3y + 2y2 = 0 + 3xy

Combine like terms: -3xy + 3xy = 0
0 + xy2 + -1x2 + -3y + 2y2 = 0 + 3xy
xy2 + -1x2 + -3y + 2y2 = 0 + 3xy
Remove the zero:
xy2 + -1x2 + -3y + 2y2 = 3xy

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

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

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

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

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

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

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

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

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

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

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

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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