12n^2-86n+14=0

Solution for 12n^2-86n+14=0 equation:

Simplifying
12n2 + -86n + 14 = 0

Reorder the terms:
14 + -86n + 12n2 = 0

Solving
14 + -86n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -43n + 6n2) = 0

Factor a trinomial.
2((1 + -6n)(7 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -6n)' equal to zero and attempt to solve:

Simplifying
1 + -6n = 0

Solving
1 + -6n = 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 + -6n = 0 + -1

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

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

Divide each side by '-6'.
n = 0.1666666667

Simplifying
n = 0.1666666667
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {0.1666666667, 7}