(4xy^2-5)dx+(4x^2y+2)dy=0

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Solution for (4xy^2-5)dx+(4x^2y+2)dy=0 equation: 


Simplifying
(4xy2 + -5) * dx + (4x2y + 2) * dy = 0

Reorder the terms:
(-5 + 4xy2) * dx + (4x2y + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(-5 + 4xy2) + (4x2y + 2) * dy = 0
(-5 * dx + 4xy2 * dx) + (4x2y + 2) * dy = 0
(-5dx + 4dx2y2) + (4x2y + 2) * dy = 0

Reorder the terms:
-5dx + 4dx2y2 + (2 + 4x2y) * dy = 0

Reorder the terms for easier multiplication:
-5dx + 4dx2y2 + dy(2 + 4x2y) = 0
-5dx + 4dx2y2 + (2 * dy + 4x2y * dy) = 0

Reorder the terms:
-5dx + 4dx2y2 + (4dx2y2 + 2dy) = 0
-5dx + 4dx2y2 + (4dx2y2 + 2dy) = 0

Combine like terms: 4dx2y2 + 4dx2y2 = 8dx2y2
-5dx + 8dx2y2 + 2dy = 0

Solving
-5dx + 8dx2y2 + 2dy = 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(-5x + 8x2y2 + 2y) = 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 '(-5x + 8x2y2 + 2y)' equal to zero and attempt to solve:

Simplifying
-5x + 8x2y2 + 2y = 0

Solving
-5x + 8x2y2 + 2y = 0

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

Add '5x' to each side of the equation.
-5x + 8x2y2 + 5x + 2y = 0 + 5x

Reorder the terms:
-5x + 5x + 8x2y2 + 2y = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + 8x2y2 + 2y = 0 + 5x
8x2y2 + 2y = 0 + 5x
Remove the zero:
8x2y2 + 2y = 5x

Add '-8x2y2' to each side of the equation.
8x2y2 + -8x2y2 + 2y = 5x + -8x2y2

Combine like terms: 8x2y2 + -8x2y2 = 0
0 + 2y = 5x + -8x2y2
2y = 5x + -8x2y2

Add '-2y' to each side of the equation.
2y + -2y = 5x + -8x2y2 + -2y

Combine like terms: 2y + -2y = 0
0 = 5x + -8x2y2 + -2y

Simplifying
0 = 5x + -8x2y2 + -2y

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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