(3(x^2)+6x(y^2))dx+(6(x^2)(y^2)+4y^3)dy=0

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Solution for (3(x^2)+6x(y^2))dx+(6(x^2)(y^2)+4y^3)dy=0 equation: 


Simplifying
(3(x2) + 6x(y2)) * dx + (6(x2)(y2) + 4y3) * dy = 0

Multiply x * y2
(3x2 + 6xy2) * dx + (6(x2)(y2) + 4y3) * dy = 0

Reorder the terms:
(6xy2 + 3x2) * dx + (6(x2)(y2) + 4y3) * dy = 0

Reorder the terms for easier multiplication:
dx(6xy2 + 3x2) + (6(x2)(y2) + 4y3) * dy = 0
(6xy2 * dx + 3x2 * dx) + (6(x2)(y2) + 4y3) * dy = 0
(6dx2y2 + 3dx3) + (6(x2)(y2) + 4y3) * dy = 0

Multiply x2 * y2
6dx2y2 + 3dx3 + (6x2y2 + 4y3) * dy = 0

Reorder the terms for easier multiplication:
6dx2y2 + 3dx3 + dy(6x2y2 + 4y3) = 0
6dx2y2 + 3dx3 + (6x2y2 * dy + 4y3 * dy) = 0
6dx2y2 + 3dx3 + (6dx2y3 + 4dy4) = 0

Reorder the terms:
6dx2y2 + 6dx2y3 + 3dx3 + 4dy4 = 0

Solving
6dx2y2 + 6dx2y3 + 3dx3 + 4dy4 = 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(6x2y2 + 6x2y3 + 3x3 + 4y4) = 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 '(6x2y2 + 6x2y3 + 3x3 + 4y4)' equal to zero and attempt to solve:

Simplifying
6x2y2 + 6x2y3 + 3x3 + 4y4 = 0

Solving
6x2y2 + 6x2y3 + 3x3 + 4y4 = 0

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

Add '-6x2y2' to each side of the equation.
6x2y2 + 6x2y3 + 3x3 + -6x2y2 + 4y4 = 0 + -6x2y2

Reorder the terms:
6x2y2 + -6x2y2 + 6x2y3 + 3x3 + 4y4 = 0 + -6x2y2

Combine like terms: 6x2y2 + -6x2y2 = 0
0 + 6x2y3 + 3x3 + 4y4 = 0 + -6x2y2
6x2y3 + 3x3 + 4y4 = 0 + -6x2y2
Remove the zero:
6x2y3 + 3x3 + 4y4 = -6x2y2

Add '-6x2y3' to each side of the equation.
6x2y3 + 3x3 + -6x2y3 + 4y4 = -6x2y2 + -6x2y3

Reorder the terms:
6x2y3 + -6x2y3 + 3x3 + 4y4 = -6x2y2 + -6x2y3

Combine like terms: 6x2y3 + -6x2y3 = 0
0 + 3x3 + 4y4 = -6x2y2 + -6x2y3
3x3 + 4y4 = -6x2y2 + -6x2y3

Add '-3x3' to each side of the equation.
3x3 + -3x3 + 4y4 = -6x2y2 + -6x2y3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 4y4 = -6x2y2 + -6x2y3 + -3x3
4y4 = -6x2y2 + -6x2y3 + -3x3

Add '-4y4' to each side of the equation.
4y4 + -4y4 = -6x2y2 + -6x2y3 + -3x3 + -4y4

Combine like terms: 4y4 + -4y4 = 0
0 = -6x2y2 + -6x2y3 + -3x3 + -4y4

Simplifying
0 = -6x2y2 + -6x2y3 + -3x3 + -4y4

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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