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.
(-17 + -2n)(6 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-8.5, 6}