3n^2-19n+16=0

Solution for 3n^2-19n+16=0 equation:

Simplifying
3n2 + -19n + 16 = 0

Reorder the terms:
16 + -19n + 3n2 = 0

Solving
16 + -19n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -1n)(16 + -3n) = 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 '(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 = {1, 5.333333333}