6n^2-21=11n

Solution for 6n^2-21=11n equation:

Simplifying
6n2 + -21 = 11n

Reorder the terms:
-21 + 6n2 = 11n

Solving
-21 + 6n2 = 11n

Solving for variable 'n'.

Reorder the terms:
-21 + -11n + 6n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
-21 + -11n + 6n2 = 0

Factor a trinomial.
(-7 + -6n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -6n)' equal to zero and attempt to solve:

Simplifying
-7 + -6n = 0

Solving
-7 + -6n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6n = 0 + 7
-6n = 0 + 7

Combine like terms: 0 + 7 = 7
-6n = 7

Divide each side by '-6'.
n = -1.166666667

Simplifying
n = -1.166666667
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 = {-1.166666667, 3}