(b-7)(b+1)=

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

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

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

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

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

Combine like terms: -7b + 1b = -6b
(-7 + -6b + b2) = 0

Solving
-7 + -6b + b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 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 + -1b = 0 + 1

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

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

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

Simplifying
b = -1
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 = {-1, 7}