-16b^4-32b^2+9=0

Solution for -16b^4-32b^2+9=0 equation:

Simplifying
-16b4 + -32b2 + 9 = 0

Reorder the terms:
9 + -32b2 + -16b4 = 0

Solving
9 + -32b2 + -16b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -4b2)(9 + 4b2) = 0

Factor a difference between two squares.
((1 + 2b)(1 + -2b))(9 + 4b2) = 0

Subproblem 1
Set the factor '(9 + 4b2)' equal to zero and attempt to solve:

Simplifying
9 + 4b2 = 0

Solving
9 + 4b2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4b2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4b2 = 0 + -9
4b2 = 0 + -9

Combine like terms: 0 + -9 = -9
4b2 = -9

Divide each side by '4'.
b2 = -2.25

Simplifying
b2 = -2.25

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 '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 0

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

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

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

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

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

Simplifying
b = -0.5
Subproblem 3
Set the factor '(1 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 0

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

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

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

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

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

Simplifying
b = 0.5
Solution
b = {-0.5, 0.5}