(b-5)(2b-1)=0

Solution for (b-5)(2b-1)=0 equation:

Simplifying
(b + -5)(2b + -1) = 0

Reorder the terms:
(-5 + b)(2b + -1) = 0

Reorder the terms:
(-5 + b)(-1 + 2b) = 0

Multiply (-5 + b) * (-1 + 2b)
(-5(-1 + 2b) + b(-1 + 2b)) = 0
((-1 * -5 + 2b * -5) + b(-1 + 2b)) = 0
((5 + -10b) + b(-1 + 2b)) = 0
(5 + -10b + (-1 * b + 2b * b)) = 0
(5 + -10b + (-1b + 2b2)) = 0

Combine like terms: -10b + -1b = -11b
(5 + -11b + 2b2) = 0

Solving
5 + -11b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -2b)(5 + -1b) = 0

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

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

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

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

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
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 = {0.5, 5}