n^2-20n+101=2

Solution for n^2-20n+101=2 equation:

Simplifying
n2 + -20n + 101 = 2

Reorder the terms:
101 + -20n + n2 = 2

Solving
101 + -20n + n2 = 2

Solving for variable 'n'.

Reorder the terms:
101 + -2 + -20n + n2 = 2 + -2

Combine like terms: 101 + -2 = 99
99 + -20n + n2 = 2 + -2

Combine like terms: 2 + -2 = 0
99 + -20n + n2 = 0

Factor a trinomial.
(9 + -1n)(11 + -1n) = 0

Subproblem 1
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
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 = {9, 11}