5n^2+48n+64=0

Solution for 5n^2+48n+64=0 equation:

Simplifying
5n2 + 48n + 64 = 0

Reorder the terms:
64 + 48n + 5n2 = 0

Solving
64 + 48n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(8 + 5n) = 0

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

Simplifying
8 + n = 0

Solving
8 + n = 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 + n = 0 + -8

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

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

Simplifying
n = -8
Subproblem 2
Set the factor '(8 + 5n)' equal to zero and attempt to solve:

Simplifying
8 + 5n = 0

Solving
8 + 5n = 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 + 5n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5n = 0 + -8
5n = 0 + -8

Combine like terms: 0 + -8 = -8
5n = -8

Divide each side by '5'.
n = -1.6

Simplifying
n = -1.6
Solution
n = {-8, -1.6}