n(n+6)=247

Solution for n(n+6)=247 equation:

Simplifying
n(n + 6) = 247

Reorder the terms:
n(6 + n) = 247
(6 * n + n * n) = 247
(6n + n2) = 247

Solving
6n + n2 = 247

Solving for variable 'n'.

Reorder the terms:
-247 + 6n + n2 = 247 + -247

Combine like terms: 247 + -247 = 0
-247 + 6n + n2 = 0

Factor a trinomial.
(-19 + -1n)(13 + -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 '(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
Solution
n = {-19, 13}