(-(3x^4+4y))dx+(-(4x+3y^3))dy=0

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Solution for (-(3x^4+4y))dx+(-(4x+3y^3))dy=0 equation: 


Simplifying
(-1(3x4 + 4y)) * dx + (-1(4x + 3y3)) * dy = 0
((3x4 * -1 + 4y * -1)) * dx + (-1(4x + 3y3)) * dy = 0
((-3x4 + -4y)) * dx + (-1(4x + 3y3)) * dy = 0

Reorder the terms for easier multiplication:
dx(-3x4 + -4y) + (-1(4x + 3y3)) * dy = 0
(-3x4 * dx + -4y * dx) + (-1(4x + 3y3)) * dy = 0

Reorder the terms:
(-4dxy + -3dx5) + (-1(4x + 3y3)) * dy = 0
(-4dxy + -3dx5) + (-1(4x + 3y3)) * dy = 0
-4dxy + -3dx5 + ((4x * -1 + 3y3 * -1)) * dy = 0
-4dxy + -3dx5 + ((-4x + -3y3)) * dy = 0

Reorder the terms for easier multiplication:
-4dxy + -3dx5 + dy(-4x + -3y3) = 0
-4dxy + -3dx5 + (-4x * dy + -3y3 * dy) = 0
-4dxy + -3dx5 + (-4dxy + -3dy4) = 0

Reorder the terms:
-4dxy + -4dxy + -3dx5 + -3dy4 = 0

Combine like terms: -4dxy + -4dxy = -8dxy
-8dxy + -3dx5 + -3dy4 = 0

Solving
-8dxy + -3dx5 + -3dy4 = 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), '-1d'.
-1d(8xy + 3x5 + 3y4) = 0

Ignore the factor -1.

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 '(8xy + 3x5 + 3y4)' equal to zero and attempt to solve:

Simplifying
8xy + 3x5 + 3y4 = 0

Solving
8xy + 3x5 + 3y4 = 0

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

Add '-8xy' to each side of the equation.
8xy + 3x5 + -8xy + 3y4 = 0 + -8xy

Reorder the terms:
8xy + -8xy + 3x5 + 3y4 = 0 + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 3x5 + 3y4 = 0 + -8xy
3x5 + 3y4 = 0 + -8xy
Remove the zero:
3x5 + 3y4 = -8xy

Add '-3x5' to each side of the equation.
3x5 + -3x5 + 3y4 = -8xy + -3x5

Combine like terms: 3x5 + -3x5 = 0
0 + 3y4 = -8xy + -3x5
3y4 = -8xy + -3x5

Add '-3y4' to each side of the equation.
3y4 + -3y4 = -8xy + -3x5 + -3y4

Combine like terms: 3y4 + -3y4 = 0
0 = -8xy + -3x5 + -3y4

Simplifying
0 = -8xy + -3x5 + -3y4

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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