(4X^3+6XY^2)DX+(6X^2Y+3Y^2)DY=0

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Solution for (4X^3+6XY^2)DX+(6X^2Y+3Y^2)DY=0 equation: 


Simplifying
(4X3 + 6XY2) * DX + (6X2Y + 3Y2) * DY = 0

Reorder the terms:
(6XY2 + 4X3) * DX + (6X2Y + 3Y2) * DY = 0

Reorder the terms for easier multiplication:
DX(6XY2 + 4X3) + (6X2Y + 3Y2) * DY = 0
(6XY2 * DX + 4X3 * DX) + (6X2Y + 3Y2) * DY = 0
(6DX2Y2 + 4DX4) + (6X2Y + 3Y2) * DY = 0

Reorder the terms for easier multiplication:
6DX2Y2 + 4DX4 + DY(6X2Y + 3Y2) = 0
6DX2Y2 + 4DX4 + (6X2Y * DY + 3Y2 * DY) = 0
6DX2Y2 + 4DX4 + (6DX2Y2 + 3DY3) = 0

Reorder the terms:
6DX2Y2 + 6DX2Y2 + 4DX4 + 3DY3 = 0

Combine like terms: 6DX2Y2 + 6DX2Y2 = 12DX2Y2
12DX2Y2 + 4DX4 + 3DY3 = 0

Solving
12DX2Y2 + 4DX4 + 3DY3 = 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(12X2Y2 + 4X4 + 3Y3) = 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 '(12X2Y2 + 4X4 + 3Y3)' equal to zero and attempt to solve:

Simplifying
12X2Y2 + 4X4 + 3Y3 = 0

Solving
12X2Y2 + 4X4 + 3Y3 = 0

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

Add '-12X2Y2' to each side of the equation.
12X2Y2 + 4X4 + -12X2Y2 + 3Y3 = 0 + -12X2Y2

Reorder the terms:
12X2Y2 + -12X2Y2 + 4X4 + 3Y3 = 0 + -12X2Y2

Combine like terms: 12X2Y2 + -12X2Y2 = 0
0 + 4X4 + 3Y3 = 0 + -12X2Y2
4X4 + 3Y3 = 0 + -12X2Y2
Remove the zero:
4X4 + 3Y3 = -12X2Y2

Add '-4X4' to each side of the equation.
4X4 + -4X4 + 3Y3 = -12X2Y2 + -4X4

Combine like terms: 4X4 + -4X4 = 0
0 + 3Y3 = -12X2Y2 + -4X4
3Y3 = -12X2Y2 + -4X4

Add '-3Y3' to each side of the equation.
3Y3 + -3Y3 = -12X2Y2 + -4X4 + -3Y3

Combine like terms: 3Y3 + -3Y3 = 0
0 = -12X2Y2 + -4X4 + -3Y3

Simplifying
0 = -12X2Y2 + -4X4 + -3Y3

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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