n(n+2)=24

Solution for n(n+2)=24 equation:

Simplifying
n(n + 2) = 24

Reorder the terms:
n(2 + n) = 24
(2 * n + n * n) = 24
(2n + n2) = 24

Solving
2n + n2 = 24

Solving for variable 'n'.

Reorder the terms:
-24 + 2n + n2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 2n + n2 = 0

Factor a trinomial.
(-6 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-6, 4}