b(b+1)=2b+1+5

Solution for b(b+1)=2b+1+5 equation:

Simplifying
b(b + 1) = 2b + 1 + 5

Reorder the terms:
b(1 + b) = 2b + 1 + 5
(1 * b + b * b) = 2b + 1 + 5
(1b + b2) = 2b + 1 + 5

Reorder the terms:
1b + b2 = 1 + 5 + 2b

Combine like terms: 1 + 5 = 6
1b + b2 = 6 + 2b

Solving
1b + b2 = 6 + 2b

Solving for variable 'b'.

Reorder the terms:
-6 + 1b + -2b + b2 = 6 + 2b + -6 + -2b

Combine like terms: 1b + -2b = -1b
-6 + -1b + b2 = 6 + 2b + -6 + -2b

Reorder the terms:
-6 + -1b + b2 = 6 + -6 + 2b + -2b

Combine like terms: 6 + -6 = 0
-6 + -1b + b2 = 0 + 2b + -2b
-6 + -1b + b2 = 2b + -2b

Combine like terms: 2b + -2b = 0
-6 + -1b + b2 = 0

Factor a trinomial.
(-2 + -1b)(3 + -1b) = 0

Subproblem 1
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
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 = {-2, 3}