2n^2-5n-102=0

Solution for 2n^2-5n-102=0 equation:

Simplifying
2n2 + -5n + -102 = 0

Reorder the terms:
-102 + -5n + 2n2 = 0

Solving
-102 + -5n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(17 + -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 '(17 + -2n)' equal to zero and attempt to solve:

Simplifying
17 + -2n = 0

Solving
17 + -2n = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2n = 0 + -17
-2n = 0 + -17

Combine like terms: 0 + -17 = -17
-2n = -17

Divide each side by '-2'.
n = 8.5

Simplifying
n = 8.5
Solution
n = {-6, 8.5}