(n+14)*(n+14)=324

Solution for (n+14)*(n+14)=324 equation:

Simplifying
(n + 14)(n + 14) = 324

Reorder the terms:
(14 + n)(n + 14) = 324

Reorder the terms:
(14 + n)(14 + n) = 324

Multiply (14 + n) * (14 + n)
(14(14 + n) + n(14 + n)) = 324
((14 * 14 + n * 14) + n(14 + n)) = 324
((196 + 14n) + n(14 + n)) = 324
(196 + 14n + (14 * n + n * n)) = 324
(196 + 14n + (14n + n2)) = 324

Combine like terms: 14n + 14n = 28n
(196 + 28n + n2) = 324

Solving
196 + 28n + n2 = 324

Solving for variable 'n'.

Reorder the terms:
196 + -324 + 28n + n2 = 324 + -324

Combine like terms: 196 + -324 = -128
-128 + 28n + n2 = 324 + -324

Combine like terms: 324 + -324 = 0
-128 + 28n + n2 = 0

Factor a trinomial.
(-32 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-32 + -1n)' equal to zero and attempt to solve:

Simplifying
-32 + -1n = 0

Solving
-32 + -1n = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1n = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1n = 0 + 32
-1n = 0 + 32

Combine like terms: 0 + 32 = 32
-1n = 32

Divide each side by '-1'.
n = -32

Simplifying
n = -32
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-32, 4}