n(n-2)+2n(n+2)=16

Solution for n(n-2)+2n(n+2)=16 equation:

Simplifying
n(n + -2) + 2n(n + 2) = 16

Reorder the terms:
n(-2 + n) + 2n(n + 2) = 16
(-2 * n + n * n) + 2n(n + 2) = 16
(-2n + n2) + 2n(n + 2) = 16

Reorder the terms:
-2n + n2 + 2n(2 + n) = 16
-2n + n2 + (2 * 2n + n * 2n) = 16
-2n + n2 + (4n + 2n2) = 16

Reorder the terms:
-2n + 4n + n2 + 2n2 = 16

Combine like terms: -2n + 4n = 2n
2n + n2 + 2n2 = 16

Combine like terms: n2 + 2n2 = 3n2
2n + 3n2 = 16

Solving
2n + 3n2 = 16

Solving for variable 'n'.

Reorder the terms:
-16 + 2n + 3n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 2n + 3n2 = 0

Factor a trinomial.
(-8 + -3n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

Solving
-8 + -3n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-2.666666667, 2}