3n^2-10n-48=0

Solution for 3n^2-10n-48=0 equation:

Simplifying
3n2 + -10n + -48 = 0

Reorder the terms:
-48 + -10n + 3n2 = 0

Solving
-48 + -10n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -3n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

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

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667
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 = {-2.666666667, 6}