(8b+1)(2b-3)=0

Solution for (8b+1)(2b-3)=0 equation:

Simplifying
(8b + 1)(2b + -3) = 0

Reorder the terms:
(1 + 8b)(2b + -3) = 0

Reorder the terms:
(1 + 8b)(-3 + 2b) = 0

Multiply (1 + 8b) * (-3 + 2b)
(1(-3 + 2b) + 8b * (-3 + 2b)) = 0
((-3 * 1 + 2b * 1) + 8b * (-3 + 2b)) = 0
((-3 + 2b) + 8b * (-3 + 2b)) = 0
(-3 + 2b + (-3 * 8b + 2b * 8b)) = 0
(-3 + 2b + (-24b + 16b2)) = 0

Combine like terms: 2b + -24b = -22b
(-3 + -22b + 16b2) = 0

Solving
-3 + -22b + 16b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -8b)(3 + -2b) = 0

Subproblem 1
Set the factor '(-1 + -8b)' equal to zero and attempt to solve:

Simplifying
-1 + -8b = 0

Solving
-1 + -8b = 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 + -8b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8b = 0 + 1
-8b = 0 + 1

Combine like terms: 0 + 1 = 1
-8b = 1

Divide each side by '-8'.
b = -0.125

Simplifying
b = -0.125
Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

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

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

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

Simplifying
b = 1.5
Solution
b = {-0.125, 1.5}