(b+4)(b+4)=100

Solution for (b+4)(b+4)=100 equation:

Simplifying
(b + 4)(b + 4) = 100

Reorder the terms:
(4 + b)(b + 4) = 100

Reorder the terms:
(4 + b)(4 + b) = 100

Multiply (4 + b) * (4 + b)
(4(4 + b) + b(4 + b)) = 100
((4 * 4 + b * 4) + b(4 + b)) = 100
((16 + 4b) + b(4 + b)) = 100
(16 + 4b + (4 * b + b * b)) = 100
(16 + 4b + (4b + b2)) = 100

Combine like terms: 4b + 4b = 8b
(16 + 8b + b2) = 100

Solving
16 + 8b + b2 = 100

Solving for variable 'b'.

Reorder the terms:
16 + -100 + 8b + b2 = 100 + -100

Combine like terms: 16 + -100 = -84
-84 + 8b + b2 = 100 + -100

Combine like terms: 100 + -100 = 0
-84 + 8b + b2 = 0

Factor a trinomial.
(-14 + -1b)(6 + -1b) = 0

Subproblem 1
Set the factor '(-14 + -1b)' equal to zero and attempt to solve:

Simplifying
-14 + -1b = 0

Solving
-14 + -1b = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1b = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1b = 0 + 14
-1b = 0 + 14

Combine like terms: 0 + 14 = 14
-1b = 14

Divide each side by '-1'.
b = -14

Simplifying
b = -14
Subproblem 2
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
Solution
b = {-14, 6}