(4b^2-3)(4b^2+1)=

Solution for (4b^2-3)(4b^2+1)= equation:

Simplifying
(4b2 + -3)(4b2 + 1) = 0

Reorder the terms:
(-3 + 4b2)(4b2 + 1) = 0

Reorder the terms:
(-3 + 4b2)(1 + 4b2) = 0

Multiply (-3 + 4b2) * (1 + 4b2)
(-3(1 + 4b2) + 4b2 * (1 + 4b2)) = 0
((1 * -3 + 4b2 * -3) + 4b2 * (1 + 4b2)) = 0
((-3 + -12b2) + 4b2 * (1 + 4b2)) = 0
(-3 + -12b2 + (1 * 4b2 + 4b2 * 4b2)) = 0
(-3 + -12b2 + (4b2 + 16b4)) = 0

Combine like terms: -12b2 + 4b2 = -8b2
(-3 + -8b2 + 16b4) = 0

Solving
-3 + -8b2 + 16b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -4b2)(3 + -4b2) = 0

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

Simplifying
-1 + -4b2 = 0

Solving
-1 + -4b2 = 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 + -4b2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4b2 = 0 + 1
-4b2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4b2 = 1

Divide each side by '-4'.
b2 = -0.25

Simplifying
b2 = -0.25

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 '(3 + -4b2)' equal to zero and attempt to solve:

Simplifying
3 + -4b2 = 0

Solving
3 + -4b2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4b2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b2 = 0 + -3
-4b2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4b2 = -3

Divide each side by '-4'.
b2 = 0.75

Simplifying
b2 = 0.75

Take the square root of each side:
b = {-0.866025404, 0.866025404}
Solution
b = {-0.866025404, 0.866025404}