(2b-5)(4-b)=0

Solution for (2b-5)(4-b)=0 equation:

Simplifying
(2b + -5)(4 + -1b) = 0

Reorder the terms:
(-5 + 2b)(4 + -1b) = 0

Multiply (-5 + 2b) * (4 + -1b)
(-5(4 + -1b) + 2b * (4 + -1b)) = 0
((4 * -5 + -1b * -5) + 2b * (4 + -1b)) = 0
((-20 + 5b) + 2b * (4 + -1b)) = 0
(-20 + 5b + (4 * 2b + -1b * 2b)) = 0
(-20 + 5b + (8b + -2b2)) = 0

Combine like terms: 5b + 8b = 13b
(-20 + 13b + -2b2) = 0

Solving
-20 + 13b + -2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-4 + b)(5 + -2b) = 0

Subproblem 1
Set the factor '(-4 + b)' equal to zero and attempt to solve:

Simplifying
-4 + b = 0

Solving
-4 + b = 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 + b = 0 + 4

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

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

Simplifying
b = 4
Subproblem 2
Set the factor '(5 + -2b)' equal to zero and attempt to solve:

Simplifying
5 + -2b = 0

Solving
5 + -2b = 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 + -2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2b = 0 + -5
-2b = 0 + -5

Combine like terms: 0 + -5 = -5
-2b = -5

Divide each side by '-2'.
b = 2.5

Simplifying
b = 2.5
Solution
b = {4, 2.5}