(b-5)(b+3)=0

Solution for (b-5)(b+3)=0 equation:

Simplifying
(b + -5)(b + 3) = 0

Reorder the terms:
(-5 + b)(b + 3) = 0

Reorder the terms:
(-5 + b)(3 + b) = 0

Multiply (-5 + b) * (3 + b)
(-5(3 + b) + b(3 + b)) = 0
((3 * -5 + b * -5) + b(3 + b)) = 0
((-15 + -5b) + b(3 + b)) = 0
(-15 + -5b + (3 * b + b * b)) = 0
(-15 + -5b + (3b + b2)) = 0

Combine like terms: -5b + 3b = -2b
(-15 + -2b + b2) = 0

Solving
-15 + -2b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -1b)(5 + -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 '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-3, 5}