(n+3)(n+3)=16

Solution for (n+3)(n+3)=16 equation:

Simplifying
(n + 3)(n + 3) = 16

Reorder the terms:
(3 + n)(n + 3) = 16

Reorder the terms:
(3 + n)(3 + n) = 16

Multiply (3 + n) * (3 + n)
(3(3 + n) + n(3 + n)) = 16
((3 * 3 + n * 3) + n(3 + n)) = 16
((9 + 3n) + n(3 + n)) = 16
(9 + 3n + (3 * n + n * n)) = 16
(9 + 3n + (3n + n2)) = 16

Combine like terms: 3n + 3n = 6n
(9 + 6n + n2) = 16

Solving
9 + 6n + n2 = 16

Solving for variable 'n'.

Reorder the terms:
9 + -16 + 6n + n2 = 16 + -16

Combine like terms: 9 + -16 = -7
-7 + 6n + n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-7 + 6n + n2 = 0

Factor a trinomial.
(-7 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-7, 1}