(X+2y)*dx-3y*dy=0

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Solution for (X+2y)*dx-3y*dy=0 equation: 


Simplifying
(X + 2y) * dx + -3y * dy = 0

Reorder the terms for easier multiplication:
dx(X + 2y) + -3y * dy = 0
(X * dx + 2y * dx) + -3y * dy = 0
(dxX + 2dxy) + -3y * dy = 0

Multiply y * dy
dxX + 2dxy + -3dy2 = 0

Solving
dxX + 2dxy + -3dy2 = 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(xX + 2xy + -3y2) = 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 '(xX + 2xy + -3y2)' equal to zero and attempt to solve:

Simplifying
xX + 2xy + -3y2 = 0

Solving
xX + 2xy + -3y2 = 0

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

Add '-1xX' to each side of the equation.
xX + 2xy + -1xX + -3y2 = 0 + -1xX

Reorder the terms:
xX + -1xX + 2xy + -3y2 = 0 + -1xX

Combine like terms: xX + -1xX = 0
0 + 2xy + -3y2 = 0 + -1xX
2xy + -3y2 = 0 + -1xX
Remove the zero:
2xy + -3y2 = -1xX

Add '-2xy' to each side of the equation.
2xy + -2xy + -3y2 = -1xX + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -3y2 = -1xX + -2xy
-3y2 = -1xX + -2xy

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -1xX + -2xy + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -1xX + -2xy + 3y2

Simplifying
0 = -1xX + -2xy + 3y2

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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