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

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

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

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

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

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

Combine like terms: -2b + -5b = -7b
(10 + -7b + b2) = 0

Solving
10 + -7b + b2 = 0

Solving for variable 'b'.

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

Subproblem 1
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
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 = {2, 5}