(b-1)(b-4)=0

Solution for (b-1)(b-4)=0 equation:

Simplifying
(b + -1)(b + -4) = 0

Reorder the terms:
(-1 + b)(b + -4) = 0

Reorder the terms:
(-1 + b)(-4 + b) = 0

Multiply (-1 + b) * (-4 + b)
(-1(-4 + b) + b(-4 + b)) = 0
((-4 * -1 + b * -1) + b(-4 + b)) = 0
((4 + -1b) + b(-4 + b)) = 0
(4 + -1b + (-4 * b + b * b)) = 0
(4 + -1b + (-4b + b2)) = 0

Combine like terms: -1b + -4b = -5b
(4 + -5b + b2) = 0

Solving
4 + -5b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -1b)(4 + -1b) = 0

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 '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {1, 4}