(b-6)*(b+3)=

Solution for (b-6)*(b+3)= equation:

Simplifying
(b + -6)(b + 3) = 0

Reorder the terms:
(-6 + b)(b + 3) = 0

Reorder the terms:
(-6 + b)(3 + b) = 0

Multiply (-6 + b) * (3 + b)
(-6(3 + b) + b(3 + b)) = 0
((3 * -6 + b * -6) + b(3 + b)) = 0
((-18 + -6b) + b(3 + b)) = 0
(-18 + -6b + (3 * b + b * b)) = 0
(-18 + -6b + (3b + b2)) = 0

Combine like terms: -6b + 3b = -3b
(-18 + -3b + b2) = 0

Solving
-18 + -3b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -1b)(6 + -1b) = 0

Subproblem 1
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
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 = {-3, 6}