7n^2-7n-14=0

Solution for 7n^2-7n-14=0 equation:

Simplifying
7n2 + -7n + -14 = 0

Reorder the terms:
-14 + -7n + 7n2 = 0

Solving
-14 + -7n + 7n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + -1n + n2) = 0

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

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

Simplifying
-1 + -1n = 0

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

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

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

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

Simplifying
n = -1
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 = {-1, 2}