(6y-24xy^6)dx+(9x-56x^2y^5)dy=0

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Solution for (6y-24xy^6)dx+(9x-56x^2y^5)dy=0 equation: 


Simplifying
(6y + -24xy6) * dx + (9x + -56x2y5) * dy = 0

Reorder the terms:
(-24xy6 + 6y) * dx + (9x + -56x2y5) * dy = 0

Reorder the terms for easier multiplication:
dx(-24xy6 + 6y) + (9x + -56x2y5) * dy = 0
(-24xy6 * dx + 6y * dx) + (9x + -56x2y5) * dy = 0

Reorder the terms:
(6dxy + -24dx2y6) + (9x + -56x2y5) * dy = 0
(6dxy + -24dx2y6) + (9x + -56x2y5) * dy = 0

Reorder the terms for easier multiplication:
6dxy + -24dx2y6 + dy(9x + -56x2y5) = 0
6dxy + -24dx2y6 + (9x * dy + -56x2y5 * dy) = 0
6dxy + -24dx2y6 + (9dxy + -56dx2y6) = 0

Reorder the terms:
6dxy + 9dxy + -24dx2y6 + -56dx2y6 = 0

Combine like terms: 6dxy + 9dxy = 15dxy
15dxy + -24dx2y6 + -56dx2y6 = 0

Combine like terms: -24dx2y6 + -56dx2y6 = -80dx2y6
15dxy + -80dx2y6 = 0

Solving
15dxy + -80dx2y6 = 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), '5dxy'.
5dxy(3 + -16xy5) = 0

Ignore the factor 5.

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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(3 + -16xy5)' equal to zero and attempt to solve:

Simplifying
3 + -16xy5 = 0

Solving
3 + -16xy5 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -16xy5 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -16xy5 = 0 + -3
-16xy5 = 0 + -3

Combine like terms: 0 + -3 = -3
-16xy5 = -3

Add '16xy5' to each side of the equation.
-16xy5 + 16xy5 = -3 + 16xy5

Combine like terms: -16xy5 + 16xy5 = 0
0 = -3 + 16xy5

Simplifying
0 = -3 + 16xy5

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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