4b(b+6)=2(b+5)+2

Solution for 4b(b+6)=2(b+5)+2 equation:

Simplifying
4b(b + 6) = 2(b + 5) + 2

Reorder the terms:
4b(6 + b) = 2(b + 5) + 2
(6 * 4b + b * 4b) = 2(b + 5) + 2
(24b + 4b2) = 2(b + 5) + 2

Reorder the terms:
24b + 4b2 = 2(5 + b) + 2
24b + 4b2 = (5 * 2 + b * 2) + 2
24b + 4b2 = (10 + 2b) + 2

Reorder the terms:
24b + 4b2 = 10 + 2 + 2b

Combine like terms: 10 + 2 = 12
24b + 4b2 = 12 + 2b

Solving
24b + 4b2 = 12 + 2b

Solving for variable 'b'.

Reorder the terms:
-12 + 24b + -2b + 4b2 = 12 + 2b + -12 + -2b

Combine like terms: 24b + -2b = 22b
-12 + 22b + 4b2 = 12 + 2b + -12 + -2b

Reorder the terms:
-12 + 22b + 4b2 = 12 + -12 + 2b + -2b

Combine like terms: 12 + -12 = 0
-12 + 22b + 4b2 = 0 + 2b + -2b
-12 + 22b + 4b2 = 2b + -2b

Combine like terms: 2b + -2b = 0
-12 + 22b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11b + 2b2) = 0

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

Ignore the factor 2.
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 '(1 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

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

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

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Solution
b = {-6, 0.5}