n(n+5)=104

Solution for n(n+5)=104 equation:

Simplifying
n(n + 5) = 104

Reorder the terms:
n(5 + n) = 104
(5 * n + n * n) = 104
(5n + n2) = 104

Solving
5n + n2 = 104

Solving for variable 'n'.

Reorder the terms:
-104 + 5n + n2 = 104 + -104

Combine like terms: 104 + -104 = 0
-104 + 5n + n2 = 0

Factor a trinomial.
(-13 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -1n)' equal to zero and attempt to solve:

Simplifying
-13 + -1n = 0

Solving
-13 + -1n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1n = 0 + 13
-1n = 0 + 13

Combine like terms: 0 + 13 = 13
-1n = 13

Divide each side by '-1'.
n = -13

Simplifying
n = -13
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-13, 8}