n(n+5)=414

Solution for n(n+5)=414 equation:

Simplifying
n(n + 5) = 414

Reorder the terms:
n(5 + n) = 414
(5 * n + n * n) = 414
(5n + n2) = 414

Solving
5n + n2 = 414

Solving for variable 'n'.

Reorder the terms:
-414 + 5n + n2 = 414 + -414

Combine like terms: 414 + -414 = 0
-414 + 5n + n2 = 0

Factor a trinomial.
(-23 + -1n)(18 + -1n) = 0

Subproblem 1
Set the factor '(-23 + -1n)' equal to zero and attempt to solve:

Simplifying
-23 + -1n = 0

Solving
-23 + -1n = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1n = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1n = 0 + 23
-1n = 0 + 23

Combine like terms: 0 + 23 = 23
-1n = 23

Divide each side by '-1'.
n = -23

Simplifying
n = -23
Subproblem 2
Set the factor '(18 + -1n)' equal to zero and attempt to solve:

Simplifying
18 + -1n = 0

Solving
18 + -1n = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1n = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1n = 0 + -18
-1n = 0 + -18

Combine like terms: 0 + -18 = -18
-1n = -18

Divide each side by '-1'.
n = 18

Simplifying
n = 18
Solution
n = {-23, 18}