12n^2-n=6

Solution for 12n^2-n=6 equation:

Simplifying
12n2 + -1n = 6

Reorder the terms:
-1n + 12n2 = 6

Solving
-1n + 12n2 = 6

Solving for variable 'n'.

Reorder the terms:
-6 + -1n + 12n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -1n + 12n2 = 0

Factor a trinomial.
(-2 + -3n)(3 + -4n) = 0

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

Simplifying
-2 + -3n = 0

Solving
-2 + -3n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3n = 0 + 2
-3n = 0 + 2

Combine like terms: 0 + 2 = 2
-3n = 2

Divide each side by '-3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

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

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

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-0.6666666667, 0.75}