2n^2-7n-114=0

Solution for 2n^2-7n-114=0 equation:

Simplifying
2n2 + -7n + -114 = 0

Reorder the terms:
-114 + -7n + 2n2 = 0

Solving
-114 + -7n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(19 + -2n) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

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

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

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(19 + -2n)' equal to zero and attempt to solve:

Simplifying
19 + -2n = 0

Solving
19 + -2n = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2n = 0 + -19
-2n = 0 + -19

Combine like terms: 0 + -19 = -19
-2n = -19

Divide each side by '-2'.
n = 9.5

Simplifying
n = 9.5
Solution
n = {-6, 9.5}