14n^2-38n-12=0

Solution for 14n^2-38n-12=0 equation:

Simplifying
14n2 + -38n + -12 = 0

Reorder the terms:
-12 + -38n + 14n2 = 0

Solving
-12 + -38n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -19n + 7n2) = 0

Factor a trinomial.
2((-2 + -7n)(3 + -1n)) = 0

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

Simplifying
-2 + -7n = 0

Solving
-2 + -7n = 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 + -7n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7n = 0 + 2
-7n = 0 + 2

Combine like terms: 0 + 2 = 2
-7n = 2

Divide each side by '-7'.
n = -0.2857142857

Simplifying
n = -0.2857142857
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 = {-0.2857142857, 3}