n(n+2)=224

Solution for n(n+2)=224 equation:

Simplifying
n(n + 2) = 224

Reorder the terms:
n(2 + n) = 224
(2 * n + n * n) = 224
(2n + n2) = 224

Solving
2n + n2 = 224

Solving for variable 'n'.

Reorder the terms:
-224 + 2n + n2 = 224 + -224

Combine like terms: 224 + -224 = 0
-224 + 2n + n2 = 0

Factor a trinomial.
(-16 + -1n)(14 + -1n) = 0

Subproblem 1
Set the factor '(-16 + -1n)' equal to zero and attempt to solve:

Simplifying
-16 + -1n = 0

Solving
-16 + -1n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1n = 0 + 16
-1n = 0 + 16

Combine like terms: 0 + 16 = 16
-1n = 16

Divide each side by '-1'.
n = -16

Simplifying
n = -16
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-16, 14}