12n^2-n-1=0

Solution for 12n^2-n-1=0 equation:

Simplifying
12n2 + -1n + -1 = 0

Reorder the terms:
-1 + -1n + 12n2 = 0

Solving
-1 + -1n + 12n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 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 + -4n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-0.25, 0.3333333333}