16b^2z^2+8bz+1=0

Solution for 16b^2z^2+8bz+1=0 equation:

Simplifying
16b2z2 + 8bz + 1 = 0

Reorder the terms:
1 + 8bz + 16b2z2 = 0

Solving
1 + 8bz + 16b2z2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + 4bz)(1 + 4bz) = 0

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

Simplifying
1 + 4bz = 0

Solving
1 + 4bz = 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 + 4bz = 0 + -1

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

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

Divide each side by '4z'.
b = -0.25z-1

Simplifying
b = -0.25z-1
Subproblem 2
Set the factor '(1 + 4bz)' equal to zero and attempt to solve:

Simplifying
1 + 4bz = 0

Solving
1 + 4bz = 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 + 4bz = 0 + -1

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

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

Divide each side by '4z'.
b = -0.25z-1

Simplifying
b = -0.25z-1
Solution
b = {-0.25z-1, -0.25z-1}