5n^2-n-48=0

Solution for 5n^2-n-48=0 equation:

Simplifying
5n2 + -1n + -48 = 0

Reorder the terms:
-48 + -1n + 5n2 = 0

Solving
-48 + -1n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(16 + -5n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(16 + -5n)' equal to zero and attempt to solve:

Simplifying
16 + -5n = 0

Solving
16 + -5n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -5n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5n = 0 + -16
-5n = 0 + -16

Combine like terms: 0 + -16 = -16
-5n = -16

Divide each side by '-5'.
n = 3.2

Simplifying
n = 3.2
Solution
n = {-3, 3.2}