5n^2-3n-8=0

Solution for 5n^2-3n-8=0 equation:

Simplifying
5n2 + -3n + -8 = 0

Reorder the terms:
-8 + -3n + 5n2 = 0

Solving
-8 + -3n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(8 + -5n) = 0

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

Simplifying
-1 + -1n = 0

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

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

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

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

Simplifying
n = -1
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 = {-1, 1.6}