5n^2-27n+34=0

Solution for 5n^2-27n+34=0 equation:

Simplifying
5n2 + -27n + 34 = 0

Reorder the terms:
34 + -27n + 5n2 = 0

Solving
34 + -27n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -1n)(17 + -5n) = 0

Subproblem 1
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
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 = {2, 3.4}