(2x+16xy)dx+(8x^2-30y^2)dy=0

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Solution for (2x+16xy)dx+(8x^2-30y^2)dy=0 equation: 


Simplifying
(2x + 16xy) * dx + (8x2 + -30y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + 16xy) + (8x2 + -30y2) * dy = 0
(2x * dx + 16xy * dx) + (8x2 + -30y2) * dy = 0
(2dx2 + 16dx2y) + (8x2 + -30y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + 16dx2y + dy(8x2 + -30y2) = 0
2dx2 + 16dx2y + (8x2 * dy + -30y2 * dy) = 0
2dx2 + 16dx2y + (8dx2y + -30dy3) = 0

Combine like terms: 16dx2y + 8dx2y = 24dx2y
2dx2 + 24dx2y + -30dy3 = 0

Solving
2dx2 + 24dx2y + -30dy3 = 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), '2d'.
2d(x2 + 12x2y + -15y3) = 0

Ignore the factor 2.

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 '(x2 + 12x2y + -15y3)' equal to zero and attempt to solve:

Simplifying
x2 + 12x2y + -15y3 = 0

Solving
x2 + 12x2y + -15y3 = 0

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

Add '-1x2' to each side of the equation.
x2 + 12x2y + -1x2 + -15y3 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 12x2y + -15y3 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 12x2y + -15y3 = 0 + -1x2
12x2y + -15y3 = 0 + -1x2
Remove the zero:
12x2y + -15y3 = -1x2

Add '-12x2y' to each side of the equation.
12x2y + -12x2y + -15y3 = -1x2 + -12x2y

Combine like terms: 12x2y + -12x2y = 0
0 + -15y3 = -1x2 + -12x2y
-15y3 = -1x2 + -12x2y

Add '15y3' to each side of the equation.
-15y3 + 15y3 = -1x2 + -12x2y + 15y3

Combine like terms: -15y3 + 15y3 = 0
0 = -1x2 + -12x2y + 15y3

Simplifying
0 = -1x2 + -12x2y + 15y3

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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