(b-3)(b+9)=0

Solution for (b-3)(b+9)=0 equation:

Simplifying
(b + -3)(b + 9) = 0

Reorder the terms:
(-3 + b)(b + 9) = 0

Reorder the terms:
(-3 + b)(9 + b) = 0

Multiply (-3 + b) * (9 + b)
(-3(9 + b) + b(9 + b)) = 0
((9 * -3 + b * -3) + b(9 + b)) = 0
((-27 + -3b) + b(9 + b)) = 0
(-27 + -3b + (9 * b + b * b)) = 0
(-27 + -3b + (9b + b2)) = 0

Combine like terms: -3b + 9b = 6b
(-27 + 6b + b2) = 0

Solving
-27 + 6b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -1b)(3 + -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 '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-9, 3}