0=3n^2-5n-12

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

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

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

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

Solving for variable 'n'.

Combine like terms: 0 + 12 = 12
12 + 5n + -3n2 = -12 + -5n + 3n2 + 12 + 5n + -3n2

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

Combine like terms: -12 + 12 = 0
12 + 5n + -3n2 = 0 + -5n + 5n + 3n2 + -3n2
12 + 5n + -3n2 = -5n + 5n + 3n2 + -3n2

Combine like terms: -5n + 5n = 0
12 + 5n + -3n2 = 0 + 3n2 + -3n2
12 + 5n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
12 + 5n + -3n2 = 0

Factor a trinomial.
(3 + -1n)(4 + 3n) = 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 '(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
Solution
n = {3, -1.333333333}