(b-7)(b+8)=0

Solution for (b-7)(b+8)=0 equation:

Simplifying
(b + -7)(b + 8) = 0

Reorder the terms:
(-7 + b)(b + 8) = 0

Reorder the terms:
(-7 + b)(8 + b) = 0

Multiply (-7 + b) * (8 + b)
(-7(8 + b) + b(8 + b)) = 0
((8 * -7 + b * -7) + b(8 + b)) = 0
((-56 + -7b) + b(8 + b)) = 0
(-56 + -7b + (8 * b + b * b)) = 0
(-56 + -7b + (8b + b2)) = 0

Combine like terms: -7b + 8b = 1b
(-56 + 1b + b2) = 0

Solving
-56 + 1b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-8 + -1b)(7 + -1b) = 0

Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve:

Simplifying
-8 + -1b = 0

Solving
-8 + -1b = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1b = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1b = 0 + 8
-1b = 0 + 8

Combine like terms: 0 + 8 = 8
-1b = 8

Divide each side by '-1'.
b = -8

Simplifying
b = -8
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-8, 7}