(D^4+5D^2+4)x=0

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Solution for (D^4+5D^2+4)x=0 equation: 


Simplifying
(D4 + 5D2 + 4) * x = 0

Reorder the terms:
(4 + 5D2 + D4) * x = 0

Reorder the terms for easier multiplication:
x(4 + 5D2 + D4) = 0
(4 * x + 5D2 * x + D4 * x) = 0
(4x + 5xD2 + xD4) = 0

Solving
4x + 5xD2 + xD4 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + 5D2 + D4) = 0

Factor a trinomial.
x((4 + D2)(1 + D2)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 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 x 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 '(1 + D2)' equal to zero and attempt to solve:

Simplifying
1 + D2 = 0

Solving
1 + D2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + D2 = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -1D2

The solution to this equation could not be determined.

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

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