3n^2-22n+32=0

Solution for 3n^2-22n+32=0 equation:

Simplifying
3n2 + -22n + 32 = 0

Reorder the terms:
32 + -22n + 3n2 = 0

Solving
32 + -22n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -1n)(16 + -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 '(16 + -3n)' equal to zero and attempt to solve:

Simplifying
16 + -3n = 0

Solving
16 + -3n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3n = 0 + -16
-3n = 0 + -16

Combine like terms: 0 + -16 = -16
-3n = -16

Divide each side by '-3'.
n = 5.333333333

Simplifying
n = 5.333333333
Solution
n = {2, 5.333333333}