(5-b)(12-2b)=0

Solution for (5-b)(12-2b)=0 equation:

Simplifying
(5 + -1b)(12 + -2b) = 0

Multiply (5 + -1b) * (12 + -2b)
(5(12 + -2b) + -1b * (12 + -2b)) = 0
((12 * 5 + -2b * 5) + -1b * (12 + -2b)) = 0
((60 + -10b) + -1b * (12 + -2b)) = 0
(60 + -10b + (12 * -1b + -2b * -1b)) = 0
(60 + -10b + (-12b + 2b2)) = 0

Combine like terms: -10b + -12b = -22b
(60 + -22b + 2b2) = 0

Solving
60 + -22b + 2b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11b + b2) = 0

Factor a trinomial.
2((5 + -1b)(6 + -1b)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {5, 6}