(n+7)(n+9)=100

Solution for (n+7)(n+9)=100 equation:

Simplifying
(n + 7)(n + 9) = 100

Reorder the terms:
(7 + n)(n + 9) = 100

Reorder the terms:
(7 + n)(9 + n) = 100

Multiply (7 + n) * (9 + n)
(7(9 + n) + n(9 + n)) = 100
((9 * 7 + n * 7) + n(9 + n)) = 100
((63 + 7n) + n(9 + n)) = 100
(63 + 7n + (9 * n + n * n)) = 100
(63 + 7n + (9n + n2)) = 100

Combine like terms: 7n + 9n = 16n
(63 + 16n + n2) = 100

Solving
63 + 16n + n2 = 100

Solving for variable 'n'.

Reorder the terms:
63 + -100 + 16n + n2 = 100 + -100

Combine like terms: 63 + -100 = -37
-37 + 16n + n2 = 100 + -100

Combine like terms: 100 + -100 = 0
-37 + 16n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 16n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + 16n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 16n + n2 = 0 + 37
16n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
16n + n2 = 37

The n term is 16n.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16n + 64 + n2 = 37 + 64

Reorder the terms:
64 + 16n + n2 = 37 + 64

Combine like terms: 37 + 64 = 101
64 + 16n + n2 = 101

Factor a perfect square on the left side:
(n + 8)(n + 8) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(n + 8) equal to 10.049875621 and -10.049875621.

Subproblem 1
n + 8 = 10.049875621

Simplifying
n + 8 = 10.049875621

Reorder the terms:
8 + n = 10.049875621

Solving
8 + n = 10.049875621

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = 10.049875621 + -8

Combine like terms: 8 + -8 = 0
0 + n = 10.049875621 + -8
n = 10.049875621 + -8

Combine like terms: 10.049875621 + -8 = 2.049875621
n = 2.049875621

Simplifying
n = 2.049875621

Subproblem 2
n + 8 = -10.049875621

Simplifying
n + 8 = -10.049875621

Reorder the terms:
8 + n = -10.049875621

Solving
8 + n = -10.049875621

Solving for variable 'n'.

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

Add '-8' to each side of the equation.
8 + -8 + n = -10.049875621 + -8

Combine like terms: 8 + -8 = 0
0 + n = -10.049875621 + -8
n = -10.049875621 + -8

Combine like terms: -10.049875621 + -8 = -18.049875621
n = -18.049875621

Simplifying
n = -18.049875621

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.049875621, -18.049875621}