(b-3)(b-5)=0

Solution for (b-3)(b-5)=0 equation:

Simplifying
(b + -3)(b + -5) = 0

Reorder the terms:
(-3 + b)(b + -5) = 0

Reorder the terms:
(-3 + b)(-5 + b) = 0

Multiply (-3 + b) * (-5 + b)
(-3(-5 + b) + b(-5 + b)) = 0
((-5 * -3 + b * -3) + b(-5 + b)) = 0
((15 + -3b) + b(-5 + b)) = 0
(15 + -3b + (-5 * b + b * b)) = 0
(15 + -3b + (-5b + b2)) = 0

Combine like terms: -3b + -5b = -8b
(15 + -8b + b2) = 0

Solving
15 + -8b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -1b)(5 + -1b) = 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 '(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
Solution
b = {3, 5}