-2n(n+8)+6(5+2n)=

Solution for -2n(n+8)+6(5+2n)= equation:

Simplifying
-2n(n + 8) + 6(5 + 2n) = 0

Reorder the terms:
-2n(8 + n) + 6(5 + 2n) = 0
(8 * -2n + n * -2n) + 6(5 + 2n) = 0
(-16n + -2n2) + 6(5 + 2n) = 0
-16n + -2n2 + (5 * 6 + 2n * 6) = 0
-16n + -2n2 + (30 + 12n) = 0

Reorder the terms:
30 + -16n + 12n + -2n2 = 0

Combine like terms: -16n + 12n = -4n
30 + -4n + -2n2 = 0

Solving
30 + -4n + -2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -2n + -1n2) = 0

Factor a trinomial.
2((3 + -1n)(5 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {3, -5}