(16D^4-40D^2+9)=0

Solution for (16D^4-40D^2+9)=0 equation:

Simplifying
(16D4 + -40D2 + 9) = 0

Reorder the terms:
(9 + -40D2 + 16D4) = 0

Remove parenthesis around (9 + -40D2 + 16D4)
9 + -40D2 + 16D4 = 0

Solving
9 + -40D2 + 16D4 = 0

Solving for variable 'D'.

Factor a trinomial.
(1 + -4D2)(9 + -4D2) = 0

Factor a difference between two squares.
((1 + 2D)(1 + -2D))(9 + -4D2) = 0

Factor a difference between two squares.
((3 + 2D)(3 + -2D))(1 + 2D)(1 + -2D) = 0

Subproblem 1
Set the factor '(1 + 2D)' equal to zero and attempt to solve:

Simplifying
1 + 2D = 0

Solving
1 + 2D = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2D = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2D = 0 + -1
2D = 0 + -1

Combine like terms: 0 + -1 = -1
2D = -1

Divide each side by '2'.
D = -0.5

Simplifying
D = -0.5
Subproblem 2
Set the factor '(1 + -2D)' equal to zero and attempt to solve:

Simplifying
1 + -2D = 0

Solving
1 + -2D = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2D = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2D = 0 + -1
-2D = 0 + -1

Combine like terms: 0 + -1 = -1
-2D = -1

Divide each side by '-2'.
D = 0.5

Simplifying
D = 0.5
Subproblem 3
Set the factor '(3 + 2D)' equal to zero and attempt to solve:

Simplifying
3 + 2D = 0

Solving
3 + 2D = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2D = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2D = 0 + -3
2D = 0 + -3

Combine like terms: 0 + -3 = -3
2D = -3

Divide each side by '2'.
D = -1.5

Simplifying
D = -1.5
Subproblem 4
Set the factor '(3 + -2D)' equal to zero and attempt to solve:

Simplifying
3 + -2D = 0

Solving
3 + -2D = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2D = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2D = 0 + -3
-2D = 0 + -3

Combine like terms: 0 + -3 = -3
-2D = -3

Divide each side by '-2'.
D = 1.5

Simplifying
D = 1.5
Solution
D = {-0.5, 0.5, -1.5, 1.5}