(DX^3-5DX^2*DY+5DX*DY^2+3DY^3)Z=0

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Solution for (DX^3-5DX^2*DY+5DX*DY^2+3DY^3)Z=0 equation: 


Simplifying
(DX3 + -5DX2 * DY + 5DX * DY2 + 3DY3) * Z = 0

Multiply DX2 * DY
(DX3 + -5D2X2Y + 5DX * DY2 + 3DY3) * Z = 0

Multiply DX * DY2
(DX3 + -5D2X2Y + 5D2XY2 + 3DY3) * Z = 0

Reorder the terms:
(DX3 + 3DY3 + 5D2XY2 + -5D2X2Y) * Z = 0

Reorder the terms for easier multiplication:
Z(DX3 + 3DY3 + 5D2XY2 + -5D2X2Y) = 0
(DX3 * Z + 3DY3 * Z + 5D2XY2 * Z + -5D2X2Y * Z) = 0
(DX3Z + 3DY3Z + 5D2XY2Z + -5D2X2YZ) = 0

Solving
DX3Z + 3DY3Z + 5D2XY2Z + -5D2X2YZ = 0

Solving for variable 'D'.

Factor out the Greatest Common Factor (GCF), 'DZ'.
DZ(X3 + 3Y3 + 5DXY2 + -5DX2Y) = 0


Subproblem 1
Set the factor 'DZ' equal to zero and attempt to solve:

Simplifying
DZ = 0

Solving
DZ = 0

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

Simplifying
DZ = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(X3 + 3Y3 + 5DXY2 + -5DX2Y)' equal to zero and attempt to solve:

Simplifying
X3 + 3Y3 + 5DXY2 + -5DX2Y = 0

Reorder the terms:
5DXY2 + -5DX2Y + X3 + 3Y3 = 0

Solving
5DXY2 + -5DX2Y + X3 + 3Y3 = 0

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

Add '-1X3' to each side of the equation.
5DXY2 + -5DX2Y + X3 + -1X3 + 3Y3 = 0 + -1X3

Combine like terms: X3 + -1X3 = 0
5DXY2 + -5DX2Y + 0 + 3Y3 = 0 + -1X3
5DXY2 + -5DX2Y + 3Y3 = 0 + -1X3
Remove the zero:
5DXY2 + -5DX2Y + 3Y3 = -1X3

Add '-3Y3' to each side of the equation.
5DXY2 + -5DX2Y + 3Y3 + -3Y3 = -1X3 + -3Y3

Combine like terms: 3Y3 + -3Y3 = 0
5DXY2 + -5DX2Y + 0 = -1X3 + -3Y3
5DXY2 + -5DX2Y = -1X3 + -3Y3

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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