(b+1)(b-6)=b-15

Solution for (b+1)(b-6)=b-15 equation:

Simplifying
(b + 1)(b + -6) = b + -15

Reorder the terms:
(1 + b)(b + -6) = b + -15

Reorder the terms:
(1 + b)(-6 + b) = b + -15

Multiply (1 + b) * (-6 + b)
(1(-6 + b) + b(-6 + b)) = b + -15
((-6 * 1 + b * 1) + b(-6 + b)) = b + -15
((-6 + 1b) + b(-6 + b)) = b + -15
(-6 + 1b + (-6 * b + b * b)) = b + -15
(-6 + 1b + (-6b + b2)) = b + -15

Combine like terms: 1b + -6b = -5b
(-6 + -5b + b2) = b + -15

Reorder the terms:
-6 + -5b + b2 = -15 + b

Solving
-6 + -5b + b2 = -15 + b

Solving for variable 'b'.

Reorder the terms:
-6 + 15 + -5b + -1b + b2 = -15 + b + 15 + -1b

Combine like terms: -6 + 15 = 9
9 + -5b + -1b + b2 = -15 + b + 15 + -1b

Combine like terms: -5b + -1b = -6b
9 + -6b + b2 = -15 + b + 15 + -1b

Reorder the terms:
9 + -6b + b2 = -15 + 15 + b + -1b

Combine like terms: -15 + 15 = 0
9 + -6b + b2 = 0 + b + -1b
9 + -6b + b2 = b + -1b

Combine like terms: b + -1b = 0
9 + -6b + b2 = 0

Factor a trinomial.
(3 + -1b)(3 + -1b) = 0

Subproblem 1
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {3, 3}