(b-2)(b+9)=0

Solution for (b-2)(b+9)=0 equation:

Simplifying
(b + -2)(b + 9) = 0

Reorder the terms:
(-2 + b)(b + 9) = 0

Reorder the terms:
(-2 + b)(9 + b) = 0

Multiply (-2 + b) * (9 + b)
(-2(9 + b) + b(9 + b)) = 0
((9 * -2 + b * -2) + b(9 + b)) = 0
((-18 + -2b) + b(9 + b)) = 0
(-18 + -2b + (9 * b + b * b)) = 0
(-18 + -2b + (9b + b2)) = 0

Combine like terms: -2b + 9b = 7b
(-18 + 7b + b2) = 0

Solving
-18 + 7b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -1b)(2 + -1b) = 0

Subproblem 1
Set the factor '(-9 + -1b)' equal to zero and attempt to solve:

Simplifying
-9 + -1b = 0

Solving
-9 + -1b = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1b = 0 + 9
-1b = 0 + 9

Combine like terms: 0 + 9 = 9
-1b = 9

Divide each side by '-1'.
b = -9

Simplifying
b = -9
Subproblem 2
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
Solution
b = {-9, 2}