(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

Reorder the terms:
(-8d2y + d4y + 16y) = 0
(-8d2y + d4y + 16y) = 0

Solving
-8d2y + d4y + 16y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8d2 + d4 + 16) = 0

Factor a trinomial.
y((d2 + -4)(d2 + -4)) = 0

Factor a difference between two squares.
y(((d + 2)(d + -2))(d2 + -4)) = 0

Factor a difference between two squares.
y(((d + 2)(d + -2))(d + 2)(d + -2)) = 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 '(d + 2)' equal to zero and attempt to solve: Simplifying d + 2 = 0 Reorder the terms: 2 + d = 0 Solving 2 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + d = 0 + -2 d = 0 + -2 Combine like terms: 0 + -2 = -2 d = -2 Simplifying d = -2

Subproblem 3

Set the factor '(d + -2)' equal to zero and attempt to solve: Simplifying d + -2 = 0 Reorder the terms: -2 + d = 0 Solving -2 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 0 + 2 Combine like terms: -2 + 2 = 0 0 + d = 0 + 2 d = 0 + 2 Combine like terms: 0 + 2 = 2 d = 2 Simplifying d = 2

Subproblem 4

Set the factor '(d + 2)' equal to zero and attempt to solve: Simplifying d + 2 = 0 Reorder the terms: 2 + d = 0 Solving 2 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + d = 0 + -2 d = 0 + -2 Combine like terms: 0 + -2 = -2 d = -2 Simplifying d = -2

Subproblem 5

Set the factor '(d + -2)' equal to zero and attempt to solve: Simplifying d + -2 = 0 Reorder the terms: -2 + d = 0 Solving -2 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 0 + 2 Combine like terms: -2 + 2 = 0 0 + d = 0 + 2 d = 0 + 2 Combine like terms: 0 + 2 = 2 d = 2 Simplifying d = 2

Solution

d = {-2, 2, -2, 2}

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