3n^2+6=11n

Solution for 3n^2+6=11n equation:

Simplifying
3n2 + 6 = 11n

Reorder the terms:
6 + 3n2 = 11n

Solving
6 + 3n2 = 11n

Solving for variable 'n'.

Reorder the terms:
6 + -11n + 3n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
6 + -11n + 3n2 = 0

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

Subproblem 1
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 2
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 = {0.6666666667, 3}