(D+2)(D^2+D-2)y=0

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


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

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

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

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

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

Reorder the terms:
y(-4 + 2D + -2D + 2D2 + D2 + D3) = 0

Combine like terms: 2D + -2D = 0
y(-4 + 0 + 2D2 + D2 + D3) = 0
y(-4 + 2D2 + D2 + D3) = 0

Combine like terms: 2D2 + D2 = 3D2
y(-4 + 3D2 + D3) = 0
(-4 * y + 3D2 * y + D3 * y) = 0
(-4y + 3yD2 + yD3) = 0

Solving
-4y + 3yD2 + yD3 = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + 3D2 + D3) = 0


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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-4 + 3D2 + D3)' equal to zero and attempt to solve:

Simplifying
-4 + 3D2 + D3 = 0

Solving
-4 + 3D2 + D3 = 0

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

Add '4' to each side of the equation.
-4 + 3D2 + 4 + D3 = 0 + 4

Reorder the terms:
-4 + 4 + 3D2 + D3 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3D2 + D3 = 0 + 4
3D2 + D3 = 0 + 4

Combine like terms: 0 + 4 = 4
3D2 + D3 = 4

Add '-3D2' to each side of the equation.
3D2 + -3D2 + D3 = 4 + -3D2

Combine like terms: 3D2 + -3D2 = 0
0 + D3 = 4 + -3D2
D3 = 4 + -3D2

Add '-1D3' to each side of the equation.
D3 + -1D3 = 4 + -3D2 + -1D3

Combine like terms: D3 + -1D3 = 0
0 = 4 + -3D2 + -1D3

Simplifying
0 = 4 + -3D2 + -1D3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}

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