(D^4+4D^2+16)Y=0

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


Simplifying
(D4 + 4D2 + 16) * Y = 0

Reorder the terms:
(16 + 4D2 + D4) * Y = 0

Reorder the terms for easier multiplication:
Y(16 + 4D2 + D4) = 0
(16 * Y + 4D2 * Y + D4 * Y) = 0

Reorder the terms:
(4D2Y + D4Y + 16Y) = 0
(4D2Y + D4Y + 16Y) = 0

Solving
4D2Y + D4Y + 16Y = 0

Solving for variable 'D'.

Factor out the Greatest Common Factor (GCF), 'Y'.
Y(4D2 + D4 + 16) = 0


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

Simplifying
Y = 0

Solving
Y = 0

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

Add '-1Y' to each side of the equation.
Y + -1Y = 0 + -1Y
Remove the zero:
0 = -1Y

Simplifying
0 = -1Y

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 '(4D2 + D4 + 16)' equal to zero and attempt to solve:

Simplifying
4D2 + D4 + 16 = 0

Reorder the terms:
16 + 4D2 + D4 = 0

Solving
16 + 4D2 + D4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 4D2 + -16 + D4 = 0 + -16

Reorder the terms:
16 + -16 + 4D2 + D4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 4D2 + D4 = 0 + -16
4D2 + D4 = 0 + -16

Combine like terms: 0 + -16 = -16
4D2 + D4 = -16

The D term is 4D2.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4D2 + 4 + D4 = -16 + 4

Reorder the terms:
4 + 4D2 + D4 = -16 + 4

Combine like terms: -16 + 4 = -12
4 + 4D2 + D4 = -12

Factor a perfect square on the left side:
(D2 + 2)(D2 + 2) = -12

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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