3n^2-5n-12=0

Solution for 3n^2-5n-12=0 equation:

Simplifying
3n2 + -5n + -12 = 0

Reorder the terms:
-12 + -5n + 3n2 = 0

Solving
-12 + -5n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -3n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve:

Simplifying
-4 + -3n = 0

Solving
-4 + -3n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3n = 0 + 4
-3n = 0 + 4

Combine like terms: 0 + 4 = 4
-3n = 4

Divide each side by '-3'.
n = -1.333333333

Simplifying
n = -1.333333333
Subproblem 2
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
Solution
n = {-1.333333333, 3}