(7b+9)(b+7)=47

Solution for (7b+9)(b+7)=47 equation:

Simplifying
(7b + 9)(b + 7) = 47

Reorder the terms:
(9 + 7b)(b + 7) = 47

Reorder the terms:
(9 + 7b)(7 + b) = 47

Multiply (9 + 7b) * (7 + b)
(9(7 + b) + 7b * (7 + b)) = 47
((7 * 9 + b * 9) + 7b * (7 + b)) = 47
((63 + 9b) + 7b * (7 + b)) = 47
(63 + 9b + (7 * 7b + b * 7b)) = 47
(63 + 9b + (49b + 7b2)) = 47

Combine like terms: 9b + 49b = 58b
(63 + 58b + 7b2) = 47

Solving
63 + 58b + 7b2 = 47

Solving for variable 'b'.

Reorder the terms:
63 + -47 + 58b + 7b2 = 47 + -47

Combine like terms: 63 + -47 = 16
16 + 58b + 7b2 = 47 + -47

Combine like terms: 47 + -47 = 0
16 + 58b + 7b2 = 0

Factor a trinomial.
(8 + b)(2 + 7b) = 0

Subproblem 1
Set the factor '(8 + b)' equal to zero and attempt to solve:

Simplifying
8 + b = 0

Solving
8 + b = 0

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

Add '-8' to each side of the equation.
8 + -8 + b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + b = 0 + -8
b = 0 + -8

Combine like terms: 0 + -8 = -8
b = -8

Simplifying
b = -8
Subproblem 2
Set the factor '(2 + 7b)' equal to zero and attempt to solve:

Simplifying
2 + 7b = 0

Solving
2 + 7b = 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 + 7b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7b = 0 + -2
7b = 0 + -2

Combine like terms: 0 + -2 = -2
7b = -2

Divide each side by '7'.
b = -0.2857142857

Simplifying
b = -0.2857142857
Solution
b = {-8, -0.2857142857}