n(n+2)=323

Solution for n(n+2)=323 equation:

Simplifying
n(n + 2) = 323

Reorder the terms:
n(2 + n) = 323
(2 * n + n * n) = 323
(2n + n2) = 323

Solving
2n + n2 = 323

Solving for variable 'n'.

Reorder the terms:
-323 + 2n + n2 = 323 + -323

Combine like terms: 323 + -323 = 0
-323 + 2n + n2 = 0

Factor a trinomial.
(-19 + -1n)(17 + -1n) = 0

Subproblem 1
Set the factor '(-19 + -1n)' equal to zero and attempt to solve:

Simplifying
-19 + -1n = 0

Solving
-19 + -1n = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1n = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1n = 0 + 19
-1n = 0 + 19

Combine like terms: 0 + 19 = 19
-1n = 19

Divide each side by '-1'.
n = -19

Simplifying
n = -19
Subproblem 2
Set the factor '(17 + -1n)' equal to zero and attempt to solve:

Simplifying
17 + -1n = 0

Solving
17 + -1n = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1n = 0 + -17
-1n = 0 + -17

Combine like terms: 0 + -17 = -17
-1n = -17

Divide each side by '-1'.
n = 17

Simplifying
n = 17
Solution
n = {-19, 17}