(7b-8)(b+5)=0

Solution for (7b-8)(b+5)=0 equation:

Simplifying
(7b + -8)(b + 5) = 0

Reorder the terms:
(-8 + 7b)(b + 5) = 0

Reorder the terms:
(-8 + 7b)(5 + b) = 0

Multiply (-8 + 7b) * (5 + b)
(-8(5 + b) + 7b * (5 + b)) = 0
((5 * -8 + b * -8) + 7b * (5 + b)) = 0
((-40 + -8b) + 7b * (5 + b)) = 0
(-40 + -8b + (5 * 7b + b * 7b)) = 0
(-40 + -8b + (35b + 7b2)) = 0

Combine like terms: -8b + 35b = 27b
(-40 + 27b + 7b2) = 0

Solving
-40 + 27b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -1b)(8 + -7b) = 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 '(8 + -7b)' equal to zero and attempt to solve:

Simplifying
8 + -7b = 0

Solving
8 + -7b = 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 + -7b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7b = 0 + -8
-7b = 0 + -8

Combine like terms: 0 + -8 = -8
-7b = -8

Divide each side by '-7'.
b = 1.142857143

Simplifying
b = 1.142857143
Solution
b = {-5, 1.142857143}