(D^4+8D^2+16)y=0

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Solution for (D^4+8D^2+16)y=0 equation: 


Simplifying
(D4 + 8D2 + 16) * y = 0

Reorder the terms:
(16 + 8D2 + D4) * y = 0

Reorder the terms for easier multiplication:
y(16 + 8D2 + D4) = 0
(16 * y + 8D2 * y + D4 * y) = 0
(16y + 8yD2 + yD4) = 0

Solving
16y + 8yD2 + yD4 = 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(16 + 8D2 + D4) = 0

Factor a trinomial.
y((4 + D2)(4 + D2)) = 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 + D2)' equal to zero and attempt to solve:

Simplifying
4 + D2 = 0

Solving
4 + D2 = 0

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

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

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

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

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

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

Simplifying
0 = -4 + -1D2

The solution to this equation could not be determined.

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

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

Simplifying
4 + D2 = 0

Solving
4 + D2 = 0

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

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

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

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

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

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

Simplifying
0 = -4 + -1D2

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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