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

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

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

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

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

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

Combine like terms: 5b + -1b = 4b
(-5 + 4b + b2) = 7

Solving
-5 + 4b + b2 = 7

Solving for variable 'b'.

Reorder the terms:
-5 + -7 + 4b + b2 = 7 + -7

Combine like terms: -5 + -7 = -12
-12 + 4b + b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-12 + 4b + b2 = 0

Factor a trinomial.
(-6 + -1b)(2 + -1b) = 0

Subproblem 1
Set the factor '(-6 + -1b)' equal to zero and attempt to solve:

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-6, 2}