n(n+13)=198

Solution for n(n+13)=198 equation:

Simplifying
n(n + 13) = 198

Reorder the terms:
n(13 + n) = 198
(13 * n + n * n) = 198
(13n + n2) = 198

Solving
13n + n2 = 198

Solving for variable 'n'.

Reorder the terms:
-198 + 13n + n2 = 198 + -198

Combine like terms: 198 + -198 = 0
-198 + 13n + n2 = 0

Factor a trinomial.
(-22 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-22 + -1n)' equal to zero and attempt to solve:

Simplifying
-22 + -1n = 0

Solving
-22 + -1n = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1n = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1n = 0 + 22
-1n = 0 + 22

Combine like terms: 0 + 22 = 22
-1n = 22

Divide each side by '-1'.
n = -22

Simplifying
n = -22
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-22, 9}