n^2-6n+11=6n

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

Simplifying
n2 + -6n + 11 = 6n

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

Solving
11 + -6n + n2 = 6n

Solving for variable 'n'.

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

Combine like terms: -6n + -6n = -12n
11 + -12n + n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
11 + -12n + n2 = 0

Factor a trinomial.
(1 + -1n)(11 + -1n) = 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 '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {1, 11}