2n(3n^2-11n+6)=0

Solution for 2n(3n^2-11n+6)=0 equation:

Simplifying
2n(3n2 + -11n + 6) = 0

Reorder the terms:
2n(6 + -11n + 3n2) = 0
(6 * 2n + -11n * 2n + 3n2 * 2n) = 0
(12n + -22n2 + 6n3) = 0

Solving
12n + -22n2 + 6n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(6 + -11n + 3n2) = 0

Factor a trinomial.
2n((2 + -3n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Subproblem 3
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0, 0.6666666667, 3}