(b-4)(b+5)=0

Solution for (b-4)(b+5)=0 equation:

Simplifying
(b + -4)(b + 5) = 0

Reorder the terms:
(-4 + b)(b + 5) = 0

Reorder the terms:
(-4 + b)(5 + b) = 0

Multiply (-4 + b) * (5 + b)
(-4(5 + b) + b(5 + b)) = 0
((5 * -4 + b * -4) + b(5 + b)) = 0
((-20 + -4b) + b(5 + b)) = 0
(-20 + -4b + (5 * b + b * b)) = 0
(-20 + -4b + (5b + b2)) = 0

Combine like terms: -4b + 5b = 1b
(-20 + 1b + b2) = 0

Solving
-20 + 1b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -1b)(4 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-5, 4}