(n+13)*(n+13)=400

Solution for (n+13)*(n+13)=400 equation:

Simplifying
(n + 13)(n + 13) = 400

Reorder the terms:
(13 + n)(n + 13) = 400

Reorder the terms:
(13 + n)(13 + n) = 400

Multiply (13 + n) * (13 + n)
(13(13 + n) + n(13 + n)) = 400
((13 * 13 + n * 13) + n(13 + n)) = 400
((169 + 13n) + n(13 + n)) = 400
(169 + 13n + (13 * n + n * n)) = 400
(169 + 13n + (13n + n2)) = 400

Combine like terms: 13n + 13n = 26n
(169 + 26n + n2) = 400

Solving
169 + 26n + n2 = 400

Solving for variable 'n'.

Reorder the terms:
169 + -400 + 26n + n2 = 400 + -400

Combine like terms: 169 + -400 = -231
-231 + 26n + n2 = 400 + -400

Combine like terms: 400 + -400 = 0
-231 + 26n + n2 = 0

Factor a trinomial.
(-33 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-33 + -1n)' equal to zero and attempt to solve:

Simplifying
-33 + -1n = 0

Solving
-33 + -1n = 0

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

Add '33' to each side of the equation.
-33 + 33 + -1n = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1n = 0 + 33
-1n = 0 + 33

Combine like terms: 0 + 33 = 33
-1n = 33

Divide each side by '-1'.
n = -33

Simplifying
n = -33
Subproblem 2
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
Solution
n = {-33, 7}