2n^2=-16n-24

Solution for 2n^2=-16n-24 equation:

Simplifying
2n2 = -16n + -24

Reorder the terms:
2n2 = -24 + -16n

Solving
2n2 = -24 + -16n

Solving for variable 'n'.

Reorder the terms:
24 + 16n + 2n2 = -24 + -16n + 24 + 16n

Reorder the terms:
24 + 16n + 2n2 = -24 + 24 + -16n + 16n

Combine like terms: -24 + 24 = 0
24 + 16n + 2n2 = 0 + -16n + 16n
24 + 16n + 2n2 = -16n + 16n

Combine like terms: -16n + 16n = 0
24 + 16n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 8n + n2) = 0

Factor a trinomial.
2((6 + n)(2 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-6, -2}