n(n+2)=399

Solution for n(n+2)=399 equation:

Simplifying
n(n + 2) = 399

Reorder the terms:
n(2 + n) = 399
(2 * n + n * n) = 399
(2n + n2) = 399

Solving
2n + n2 = 399

Solving for variable 'n'.

Reorder the terms:
-399 + 2n + n2 = 399 + -399

Combine like terms: 399 + -399 = 0
-399 + 2n + n2 = 0

Factor a trinomial.
(-21 + -1n)(19 + -1n) = 0

Subproblem 1
Set the factor '(-21 + -1n)' equal to zero and attempt to solve:

Simplifying
-21 + -1n = 0

Solving
-21 + -1n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1n = 0 + 21
-1n = 0 + 21

Combine like terms: 0 + 21 = 21
-1n = 21

Divide each side by '-1'.
n = -21

Simplifying
n = -21
Subproblem 2
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
Solution
n = {-21, 19}