(b+9)(b-6)=0

Solution for (b+9)(b-6)=0 equation:

Simplifying
(b + 9)(b + -6) = 0

Reorder the terms:
(9 + b)(b + -6) = 0

Reorder the terms:
(9 + b)(-6 + b) = 0

Multiply (9 + b) * (-6 + b)
(9(-6 + b) + b(-6 + b)) = 0
((-6 * 9 + b * 9) + b(-6 + b)) = 0
((-54 + 9b) + b(-6 + b)) = 0
(-54 + 9b + (-6 * b + b * b)) = 0
(-54 + 9b + (-6b + b2)) = 0

Combine like terms: 9b + -6b = 3b
(-54 + 3b + b2) = 0

Solving
-54 + 3b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -1b)(6 + -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 '(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 = {-9, 6}