12n^2+64n=-20

Solution for 12n^2+64n=-20 equation:

Simplifying
12n2 + 64n = -20

Reorder the terms:
64n + 12n2 = -20

Solving
64n + 12n2 = -20

Solving for variable 'n'.

Reorder the terms:
20 + 64n + 12n2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 64n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 16n + 3n2) = 0

Factor a trinomial.
4((5 + n)(1 + 3n)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 0

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

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

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

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

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {-5, -0.3333333333}