5n^2-12n-17=0

Solution for 5n^2-12n-17=0 equation:

Simplifying
5n2 + -12n + -17 = 0

Reorder the terms:
-17 + -12n + 5n2 = 0

Solving
-17 + -12n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(17 + -5n) = 0

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 '(17 + -5n)' equal to zero and attempt to solve:

Simplifying
17 + -5n = 0

Solving
17 + -5n = 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 + -5n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -5n = 0 + -17
-5n = 0 + -17

Combine like terms: 0 + -17 = -17
-5n = -17

Divide each side by '-5'.
n = 3.4

Simplifying
n = 3.4
Solution
n = {-1, 3.4}