(D-2)(D^2-2D)Y=0

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Solution for (D-2)(D^2-2D)Y=0 equation: 


Simplifying
(D + -2)(D2 + -2D) * Y = 0

Reorder the terms:
(-2 + D)(D2 + -2D) * Y = 0

Reorder the terms:
(-2 + D)(-2D + D2) * Y = 0

Reorder the terms for easier multiplication:
Y(-2 + D)(-2D + D2) = 0

Multiply (-2 + D) * (-2D + D2)
Y(-2(-2D + D2) + D(-2D + D2)) = 0
Y((-2D * -2 + D2 * -2) + D(-2D + D2)) = 0
Y((4D + -2D2) + D(-2D + D2)) = 0
Y(4D + -2D2 + (-2D * D + D2 * D)) = 0
Y(4D + -2D2 + (-2D2 + D3)) = 0

Combine like terms: -2D2 + -2D2 = -4D2
Y(4D + -4D2 + D3) = 0
(4D * Y + -4D2 * Y + D3 * Y) = 0
(4DY + -4D2Y + D3Y) = 0

Solving
4DY + -4D2Y + D3Y = 0

Solving for variable 'D'.

Factor out the Greatest Common Factor (GCF), 'DY'.
DY(4 + -4D + D2) = 0

Factor a trinomial.
DY((2 + -1D)(2 + -1D)) = 0


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

Simplifying
DY = 0

Solving
DY = 0

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

Simplifying
DY = 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 '(2 + -1D)' equal to zero and attempt to solve:

Simplifying
2 + -1D = 0

Solving
2 + -1D = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1D = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1D = 0 + -2
-1D = 0 + -2

Combine like terms: 0 + -2 = -2
-1D = -2

Divide each side by '-1'.
D = 2

Simplifying
D = 2

Subproblem 3
Set the factor '(2 + -1D)' equal to zero and attempt to solve:

Simplifying
2 + -1D = 0

Solving
2 + -1D = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1D = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1D = 0 + -2
-1D = 0 + -2

Combine like terms: 0 + -2 = -2
-1D = -2

Divide each side by '-1'.
D = 2

Simplifying
D = 2
Solution
D = {2, 2}

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