(D^3+D^2+D+6)y=0

Solution for (D^3+D^2+D+6)y=0 equation:

Simplifying
(D3 + D2 + D + 6) * y = 0

Reorder the terms:
(6 + D + D2 + D3) * y = 0

Reorder the terms for easier multiplication:
y(6 + D + D2 + D3) = 0
(6 * y + D * y + D2 * y + D3 * y) = 0
(6y + yD + yD2 + yD3) = 0

Solving
6y + yD + yD2 + 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(6 + D + D2 + 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 '(6 + D + D2 + D3)' equal to zero and attempt to solve:

Simplifying
6 + D + D2 + D3 = 0

Solving
6 + D + D2 + D3 = 0

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

Add '-6' to each side of the equation.
6 + D + D2 + -6 + D3 = 0 + -6

Reorder the terms:
6 + -6 + D + D2 + D3 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + D + D2 + D3 = 0 + -6
D + D2 + D3 = 0 + -6

Combine like terms: 0 + -6 = -6
D + D2 + D3 = -6

Add '-1D' to each side of the equation.
D + D2 + -1D + D3 = -6 + -1D

Reorder the terms:
D + -1D + D2 + D3 = -6 + -1D

Combine like terms: D + -1D = 0
0 + D2 + D3 = -6 + -1D
D2 + D3 = -6 + -1D

Add '-1D2' to each side of the equation.
D2 + -1D2 + D3 = -6 + -1D + -1D2

Combine like terms: D2 + -1D2 = 0
0 + D3 = -6 + -1D + -1D2
D3 = -6 + -1D + -1D2

Add '-1D3' to each side of the equation.
D3 + -1D3 = -6 + -1D + -1D2 + -1D3

Combine like terms: D3 + -1D3 = 0
0 = -6 + -1D + -1D2 + -1D3

Simplifying
0 = -6 + -1D + -1D2 + -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}