(-20xy^2+6)dx+(3y^2-20x^2y)dy=0

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Solution for (-20xy^2+6)dx+(3y^2-20x^2y)dy=0 equation: 


Simplifying
(-20xy2 + 6) * dx + (3y2 + -20x2y) * dy = 0

Reorder the terms:
(6 + -20xy2) * dx + (3y2 + -20x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(6 + -20xy2) + (3y2 + -20x2y) * dy = 0
(6 * dx + -20xy2 * dx) + (3y2 + -20x2y) * dy = 0
(6dx + -20dx2y2) + (3y2 + -20x2y) * dy = 0

Reorder the terms:
6dx + -20dx2y2 + (-20x2y + 3y2) * dy = 0

Reorder the terms for easier multiplication:
6dx + -20dx2y2 + dy(-20x2y + 3y2) = 0
6dx + -20dx2y2 + (-20x2y * dy + 3y2 * dy) = 0
6dx + -20dx2y2 + (-20dx2y2 + 3dy3) = 0

Combine like terms: -20dx2y2 + -20dx2y2 = -40dx2y2
6dx + -40dx2y2 + 3dy3 = 0

Solving
6dx + -40dx2y2 + 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(6x + -40x2y2 + 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 '(6x + -40x2y2 + 3y3)' equal to zero and attempt to solve:

Simplifying
6x + -40x2y2 + 3y3 = 0

Solving
6x + -40x2y2 + 3y3 = 0

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

Add '-6x' to each side of the equation.
6x + -40x2y2 + -6x + 3y3 = 0 + -6x

Reorder the terms:
6x + -6x + -40x2y2 + 3y3 = 0 + -6x

Combine like terms: 6x + -6x = 0
0 + -40x2y2 + 3y3 = 0 + -6x
-40x2y2 + 3y3 = 0 + -6x
Remove the zero:
-40x2y2 + 3y3 = -6x

Add '40x2y2' to each side of the equation.
-40x2y2 + 40x2y2 + 3y3 = -6x + 40x2y2

Combine like terms: -40x2y2 + 40x2y2 = 0
0 + 3y3 = -6x + 40x2y2
3y3 = -6x + 40x2y2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -6x + 40x2y2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -6x + 40x2y2 + -3y3

Simplifying
0 = -6x + 40x2y2 + -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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