5n^2+2n-192=0

Solution for 5n^2+2n-192=0 equation:

Simplifying
5n2 + 2n + -192 = 0

Reorder the terms:
-192 + 2n + 5n2 = 0

Solving
-192 + 2n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-32 + -5n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-32 + -5n)' equal to zero and attempt to solve:

Simplifying
-32 + -5n = 0

Solving
-32 + -5n = 0

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

Add '32' to each side of the equation.
-32 + 32 + -5n = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -5n = 0 + 32
-5n = 0 + 32

Combine like terms: 0 + 32 = 32
-5n = 32

Divide each side by '-5'.
n = -6.4

Simplifying
n = -6.4
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-6.4, 6}