(n+3)(n+3)=64

Solution for (n+3)(n+3)=64 equation:

Simplifying
(n + 3)(n + 3) = 64

Reorder the terms:
(3 + n)(n + 3) = 64

Reorder the terms:
(3 + n)(3 + n) = 64

Multiply (3 + n) * (3 + n)
(3(3 + n) + n(3 + n)) = 64
((3 * 3 + n * 3) + n(3 + n)) = 64
((9 + 3n) + n(3 + n)) = 64
(9 + 3n + (3 * n + n * n)) = 64
(9 + 3n + (3n + n2)) = 64

Combine like terms: 3n + 3n = 6n
(9 + 6n + n2) = 64

Solving
9 + 6n + n2 = 64

Solving for variable 'n'.

Reorder the terms:
9 + -64 + 6n + n2 = 64 + -64

Combine like terms: 9 + -64 = -55
-55 + 6n + n2 = 64 + -64

Combine like terms: 64 + -64 = 0
-55 + 6n + n2 = 0

Factor a trinomial.
(-11 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve:

Simplifying
-11 + -1n = 0

Solving
-11 + -1n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1n = 0 + 11
-1n = 0 + 11

Combine like terms: 0 + 11 = 11
-1n = 11

Divide each side by '-1'.
n = -11

Simplifying
n = -11
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-11, 5}