n(n+2)=120

Solution for n(n+2)=120 equation:

Simplifying
n(n + 2) = 120

Reorder the terms:
n(2 + n) = 120
(2 * n + n * n) = 120
(2n + n2) = 120

Solving
2n + n2 = 120

Solving for variable 'n'.

Reorder the terms:
-120 + 2n + n2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 2n + n2 = 0

Factor a trinomial.
(-12 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1n = 0 + 12
-1n = 0 + 12

Combine like terms: 0 + 12 = 12
-1n = 12

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-12, 10}