(b-8)(b-5)=0

Solution for (b-8)(b-5)=0 equation:

Simplifying
(b + -8)(b + -5) = 0

Reorder the terms:
(-8 + b)(b + -5) = 0

Reorder the terms:
(-8 + b)(-5 + b) = 0

Multiply (-8 + b) * (-5 + b)
(-8(-5 + b) + b(-5 + b)) = 0
((-5 * -8 + b * -8) + b(-5 + b)) = 0
((40 + -8b) + b(-5 + b)) = 0
(40 + -8b + (-5 * b + b * b)) = 0
(40 + -8b + (-5b + b2)) = 0

Combine like terms: -8b + -5b = -13b
(40 + -13b + b2) = 0

Solving
40 + -13b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(5 + -1b)(8 + -1b) = 0

Subproblem 1
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve:

Simplifying
8 + -1b = 0

Solving
8 + -1b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1b = 0 + -8

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

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

Divide each side by '-1'.
b = 8

Simplifying
b = 8
Solution
b = {5, 8}