3(b-1)(b-5)=0

Solution for 3(b-1)(b-5)=0 equation:

Simplifying
3(b + -1)(b + -5) = 0

Reorder the terms:
3(-1 + b)(b + -5) = 0

Reorder the terms:
3(-1 + b)(-5 + b) = 0

Multiply (-1 + b) * (-5 + b)
3(-1(-5 + b) + b(-5 + b)) = 0
3((-5 * -1 + b * -1) + b(-5 + b)) = 0
3((5 + -1b) + b(-5 + b)) = 0
3(5 + -1b + (-5 * b + b * b)) = 0
3(5 + -1b + (-5b + b2)) = 0

Combine like terms: -1b + -5b = -6b
3(5 + -6b + b2) = 0
(5 * 3 + -6b * 3 + b2 * 3) = 0
(15 + -18b + 3b2) = 0

Solving
15 + -18b + 3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -6b + b2) = 0

Factor a trinomial.
3((1 + -1b)(5 + -1b)) = 0

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

Simplifying
1 + -1b = 0

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

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

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

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

Simplifying
b = 1
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 = {1, 5}