(b+10)(b-12)=0

Solution for (b+10)(b-12)=0 equation:

Simplifying
(b + 10)(b + -12) = 0

Reorder the terms:
(10 + b)(b + -12) = 0

Reorder the terms:
(10 + b)(-12 + b) = 0

Multiply (10 + b) * (-12 + b)
(10(-12 + b) + b(-12 + b)) = 0
((-12 * 10 + b * 10) + b(-12 + b)) = 0
((-120 + 10b) + b(-12 + b)) = 0
(-120 + 10b + (-12 * b + b * b)) = 0
(-120 + 10b + (-12b + b2)) = 0

Combine like terms: 10b + -12b = -2b
(-120 + -2b + b2) = 0

Solving
-120 + -2b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-10 + -1b)(12 + -1b) = 0

Subproblem 1
Set the factor '(-10 + -1b)' equal to zero and attempt to solve:

Simplifying
-10 + -1b = 0

Solving
-10 + -1b = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1b = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1b = 0 + 10
-1b = 0 + 10

Combine like terms: 0 + 10 = 10
-1b = 10

Divide each side by '-1'.
b = -10

Simplifying
b = -10
Subproblem 2
Set the factor '(12 + -1b)' equal to zero and attempt to solve:

Simplifying
12 + -1b = 0

Solving
12 + -1b = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1b = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1b = 0 + -12
-1b = 0 + -12

Combine like terms: 0 + -12 = -12
-1b = -12

Divide each side by '-1'.
b = 12

Simplifying
b = 12
Solution
b = {-10, 12}