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

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

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

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

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

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

Combine like terms: 24b + -1b = 23b
(-3 + 23b + 8b2) = 0

Solving
-3 + 23b + 8b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 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 + -1b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1b = 0 + 3
-1b = 0 + 3

Combine like terms: 0 + 3 = 3
-1b = 3

Divide each side by '-1'.
b = -3

Simplifying
b = -3
Subproblem 2
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
Solution
b = {-3, 0.125}