1+2b(b+6)=5(b-1)

Solution for 1+2b(b+6)=5(b-1) equation:

Simplifying
1 + 2b(b + 6) = 5(b + -1)

Reorder the terms:
1 + 2b(6 + b) = 5(b + -1)
1 + (6 * 2b + b * 2b) = 5(b + -1)
1 + (12b + 2b2) = 5(b + -1)

Reorder the terms:
1 + 12b + 2b2 = 5(-1 + b)
1 + 12b + 2b2 = (-1 * 5 + b * 5)
1 + 12b + 2b2 = (-5 + 5b)

Solving
1 + 12b + 2b2 = -5 + 5b

Solving for variable 'b'.

Reorder the terms:
1 + 5 + 12b + -5b + 2b2 = -5 + 5b + 5 + -5b

Combine like terms: 1 + 5 = 6
6 + 12b + -5b + 2b2 = -5 + 5b + 5 + -5b

Combine like terms: 12b + -5b = 7b
6 + 7b + 2b2 = -5 + 5b + 5 + -5b

Reorder the terms:
6 + 7b + 2b2 = -5 + 5 + 5b + -5b

Combine like terms: -5 + 5 = 0
6 + 7b + 2b2 = 0 + 5b + -5b
6 + 7b + 2b2 = 5b + -5b

Combine like terms: 5b + -5b = 0
6 + 7b + 2b2 = 0

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

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

Simplifying
2 + b = 0

Solving
2 + b = 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 + b = 0 + -2

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

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

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

Simplifying
3 + 2b = 0

Solving
3 + 2b = 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 + 2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2b = 0 + -3
2b = 0 + -3

Combine like terms: 0 + -3 = -3
2b = -3

Divide each side by '2'.
b = -1.5

Simplifying
b = -1.5
Solution
b = {-2, -1.5}