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

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


Simplifying
(3X2 + 4XY) * dx + (2x + 2y) * dy = 0

Reorder the terms:
(4XY + 3X2) * dx + (2x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(4XY + 3X2) + (2x + 2y) * dy = 0
(4XY * dx + 3X2 * dx) + (2x + 2y) * dy = 0
(4dxXY + 3dxX2) + (2x + 2y) * dy = 0

Reorder the terms for easier multiplication:
4dxXY + 3dxX2 + dy(2x + 2y) = 0
4dxXY + 3dxX2 + (2x * dy + 2y * dy) = 0
4dxXY + 3dxX2 + (2dxy + 2dy2) = 0

Solving
4dxXY + 3dxX2 + 2dxy + 2dy2 = 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(4xXY + 3xX2 + 2xy + 2y2) = 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 '(4xXY + 3xX2 + 2xy + 2y2)' equal to zero and attempt to solve:

Simplifying
4xXY + 3xX2 + 2xy + 2y2 = 0

Solving
4xXY + 3xX2 + 2xy + 2y2 = 0

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

Add '-4xXY' to each side of the equation.
4xXY + 3xX2 + 2xy + -4xXY + 2y2 = 0 + -4xXY

Reorder the terms:
4xXY + -4xXY + 3xX2 + 2xy + 2y2 = 0 + -4xXY

Combine like terms: 4xXY + -4xXY = 0
0 + 3xX2 + 2xy + 2y2 = 0 + -4xXY
3xX2 + 2xy + 2y2 = 0 + -4xXY
Remove the zero:
3xX2 + 2xy + 2y2 = -4xXY

Add '-3xX2' to each side of the equation.
3xX2 + 2xy + -3xX2 + 2y2 = -4xXY + -3xX2

Reorder the terms:
3xX2 + -3xX2 + 2xy + 2y2 = -4xXY + -3xX2

Combine like terms: 3xX2 + -3xX2 = 0
0 + 2xy + 2y2 = -4xXY + -3xX2
2xy + 2y2 = -4xXY + -3xX2

Add '-2xy' to each side of the equation.
2xy + -2xy + 2y2 = -4xXY + -3xX2 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 2y2 = -4xXY + -3xX2 + -2xy
2y2 = -4xXY + -3xX2 + -2xy

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -4xXY + -3xX2 + -2xy + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -4xXY + -3xX2 + -2xy + -2y2

Simplifying
0 = -4xXY + -3xX2 + -2xy + -2y2

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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