-11+12n=2n-n^2

Solution for -11+12n=2n-n^2 equation:

Simplifying
-11 + 12n = 2n + -1n2

Solving
-11 + 12n = 2n + -1n2

Solving for variable 'n'.

Combine like terms: 12n + -2n = 10n
-11 + 10n + n2 = 2n + -1n2 + -2n + n2

Reorder the terms:
-11 + 10n + n2 = 2n + -2n + -1n2 + n2

Combine like terms: 2n + -2n = 0
-11 + 10n + n2 = 0 + -1n2 + n2
-11 + 10n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-11 + 10n + n2 = 0

Factor a trinomial.
(-11 + -1n)(1 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-11, 1}