3n^2-17n+22=0

Solution for 3n^2-17n+22=0 equation:

Simplifying
3n2 + -17n + 22 = 0

Reorder the terms:
22 + -17n + 3n2 = 0

Solving
22 + -17n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -1n)(11 + -3n) = 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 '(11 + -3n)' equal to zero and attempt to solve:

Simplifying
11 + -3n = 0

Solving
11 + -3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3n = 0 + -11
-3n = 0 + -11

Combine like terms: 0 + -11 = -11
-3n = -11

Divide each side by '-3'.
n = 3.666666667

Simplifying
n = 3.666666667
Solution
n = {2, 3.666666667}