((x^7)+(y^7))dx+(dy(7xy^6))=0

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Solution for ((x^7)+(y^7))dx+(dy(7xy^6))=0 equation: 


Simplifying
((x7) + (y7)) * dx + (dy(7xy6)) = 0
(x7 + (y7)) * dx + (dy(7xy6)) = 0
(x7 + y7) * dx + (dy(7xy6)) = 0

Reorder the terms for easier multiplication:
dx(x7 + y7) + (dy(7xy6)) = 0
(x7 * dx + y7 * dx) + (dy(7xy6)) = 0

Reorder the terms:
(dxy7 + dx8) + (dy(7xy6)) = 0
(dxy7 + dx8) + (dy(7xy6)) = 0

Remove parenthesis around (7xy6)
dxy7 + dx8 + (dy * 7xy6) = 0

Reorder the terms for easier multiplication:
dxy7 + dx8 + (7dy * xy6) = 0

Multiply dy * xy6
dxy7 + dx8 + (7dxy7) = 0

Reorder the terms:
dxy7 + (7dxy7) + dx8 = 0

Combine like terms: dxy7 + (7dxy7) = 8dxy7
8dxy7 + dx8 = 0

Solving
8dxy7 + dx8 = 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), 'dx'.
dx(8y7 + x7) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(8y7 + x7)' equal to zero and attempt to solve:

Simplifying
8y7 + x7 = 0

Reorder the terms:
x7 + 8y7 = 0

Solving
x7 + 8y7 = 0

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

Add '-1x7' to each side of the equation.
x7 + -1x7 + 8y7 = 0 + -1x7

Combine like terms: x7 + -1x7 = 0
0 + 8y7 = 0 + -1x7
8y7 = 0 + -1x7
Remove the zero:
8y7 = -1x7

Add '-8y7' to each side of the equation.
8y7 + -8y7 = -1x7 + -8y7

Combine like terms: 8y7 + -8y7 = 0
0 = -1x7 + -8y7

Simplifying
0 = -1x7 + -8y7

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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