2(7n^2-13n-2)=0

Solution for 2(7n^2-13n-2)=0 equation:

Simplifying
2(7n2 + -13n + -2) = 0

Reorder the terms:
2(-2 + -13n + 7n2) = 0
(-2 * 2 + -13n * 2 + 7n2 * 2) = 0
(-4 + -26n + 14n2) = 0

Solving
-4 + -26n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -13n + 7n2) = 0

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

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

Simplifying
-1 + -7n = 0

Solving
-1 + -7n = 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 + -7n = 0 + 1

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

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

Divide each side by '-7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-0.1428571429, 2}