(7b+1)(b-5)=0

Solution for (7b+1)(b-5)=0 equation:

Simplifying
(7b + 1)(b + -5) = 0

Reorder the terms:
(1 + 7b)(b + -5) = 0

Reorder the terms:
(1 + 7b)(-5 + b) = 0

Multiply (1 + 7b) * (-5 + b)
(1(-5 + b) + 7b * (-5 + b)) = 0
((-5 * 1 + b * 1) + 7b * (-5 + b)) = 0
((-5 + 1b) + 7b * (-5 + b)) = 0
(-5 + 1b + (-5 * 7b + b * 7b)) = 0
(-5 + 1b + (-35b + 7b2)) = 0

Combine like terms: 1b + -35b = -34b
(-5 + -34b + 7b2) = 0

Solving
-5 + -34b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -7b)(5 + -1b) = 0

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

Simplifying
-1 + -7b = 0

Solving
-1 + -7b = 0

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

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

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

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

Divide each side by '-7'.
b = -0.1428571429

Simplifying
b = -0.1428571429
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 = {-0.1428571429, 5}