(7x+4y)dx+(4y-8y^3)dy=0

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Solution for (7x+4y)dx+(4y-8y^3)dy=0 equation: 


Simplifying
(7x + 4y) * dx + (4y + -8y3) * dy = 0

Reorder the terms for easier multiplication:
dx(7x + 4y) + (4y + -8y3) * dy = 0
(7x * dx + 4y * dx) + (4y + -8y3) * dy = 0

Reorder the terms:
(4dxy + 7dx2) + (4y + -8y3) * dy = 0
(4dxy + 7dx2) + (4y + -8y3) * dy = 0

Reorder the terms for easier multiplication:
4dxy + 7dx2 + dy(4y + -8y3) = 0
4dxy + 7dx2 + (4y * dy + -8y3 * dy) = 0
4dxy + 7dx2 + (4dy2 + -8dy4) = 0

Solving
4dxy + 7dx2 + 4dy2 + -8dy4 = 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(4xy + 7x2 + 4y2 + -8y4) = 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 '(4xy + 7x2 + 4y2 + -8y4)' equal to zero and attempt to solve:

Simplifying
4xy + 7x2 + 4y2 + -8y4 = 0

Solving
4xy + 7x2 + 4y2 + -8y4 = 0

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

Add '-4xy' to each side of the equation.
4xy + 7x2 + 4y2 + -4xy + -8y4 = 0 + -4xy

Reorder the terms:
4xy + -4xy + 7x2 + 4y2 + -8y4 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 7x2 + 4y2 + -8y4 = 0 + -4xy
7x2 + 4y2 + -8y4 = 0 + -4xy
Remove the zero:
7x2 + 4y2 + -8y4 = -4xy

Add '-7x2' to each side of the equation.
7x2 + 4y2 + -7x2 + -8y4 = -4xy + -7x2

Reorder the terms:
7x2 + -7x2 + 4y2 + -8y4 = -4xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 + 4y2 + -8y4 = -4xy + -7x2
4y2 + -8y4 = -4xy + -7x2

Add '-4y2' to each side of the equation.
4y2 + -4y2 + -8y4 = -4xy + -7x2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 + -8y4 = -4xy + -7x2 + -4y2
-8y4 = -4xy + -7x2 + -4y2

Add '8y4' to each side of the equation.
-8y4 + 8y4 = -4xy + -7x2 + -4y2 + 8y4

Combine like terms: -8y4 + 8y4 = 0
0 = -4xy + -7x2 + -4y2 + 8y4

Simplifying
0 = -4xy + -7x2 + -4y2 + 8y4

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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