(b-1)(b-2)=0

Solution for (b-1)(b-2)=0 equation:

Simplifying
(b + -1)(b + -2) = 0

Reorder the terms:
(-1 + b)(b + -2) = 0

Reorder the terms:
(-1 + b)(-2 + b) = 0

Multiply (-1 + b) * (-2 + b)
(-1(-2 + b) + b(-2 + b)) = 0
((-2 * -1 + b * -1) + b(-2 + b)) = 0
((2 + -1b) + b(-2 + b)) = 0
(2 + -1b + (-2 * b + b * b)) = 0
(2 + -1b + (-2b + b2)) = 0

Combine like terms: -1b + -2b = -3b
(2 + -3b + b2) = 0

Solving
2 + -3b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -1b)(2 + -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 '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {1, 2}