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

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


Simplifying
(3x2) + (2y2) * dx + ((4xy + 6y2) * dy) = 0

Remove parenthesis around (2y2)
(3x2) + 2y2 * dx + ((4xy + 6y2) * dy) = 0

Multiply y2 * dx
(3x2) + 2dxy2 + ((4xy + 6y2) * dy) = 0

Reorder the terms for easier multiplication:
(3x2) + 2dxy2 + (dy(4xy + 6y2)) = 0
(3x2) + 2dxy2 + ((4xy * dy + 6y2 * dy)) = 0
(3x2) + 2dxy2 + ((4dxy2 + 6dy3)) = 0
(3x2) + 2dxy2 + (4dxy2 + 6dy3) = 0

Remove parenthesis around (4dxy2 + 6dy3)
(3x2) + 2dxy2 + 4dxy2 + 6dy3 = 0

Reorder the terms:
2dxy2 + 4dxy2 + 6dy3 + (3x2) = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
6dxy2 + 6dy3 + (3x2) = 0

Solving
6dxy2 + 6dy3 + (3x2) = 0

Solving for variable 'd'.

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

Add '(-3x2)' to each side of the equation.
6dxy2 + 6dy3 + (3x2) + (-3x2) = 0 + (-3x2)

Combine like terms: (3x2) + (-3x2) = 0
6dxy2 + 6dy3 + 0 = 0 + (-3x2)
6dxy2 + 6dy3 = 0 + (-3x2)
Remove the zero:
6dxy2 + 6dy3 = (-3x2)

Combine like terms: (-3x2) + (3x2) = 0
6dxy2 + 6dy3 + (3x2) = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2dxy2 + 2dy3 + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2dxy2 + 2dy3 + x2)' equal to zero and attempt to solve:

Simplifying
2dxy2 + 2dy3 + x2 = 0

Solving
2dxy2 + 2dy3 + x2 = 0

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

Add '-1x2' to each side of the equation.
2dxy2 + 2dy3 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
2dxy2 + 2dy3 + 0 = 0 + -1x2
2dxy2 + 2dy3 = 0 + -1x2
Remove the zero:
2dxy2 + 2dy3 = -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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