81=-n^2-2n+21

Solution for 81=-n^2-2n+21 equation:

Simplifying
81 = -1n2 + -2n + 21

Reorder the terms:
81 = 21 + -2n + -1n2

Solving
81 = 21 + -2n + -1n2

Solving for variable 'n'.

Combine like terms: 81 + -21 = 60
60 + 2n + n2 = 21 + -2n + -1n2 + -21 + 2n + n2

Reorder the terms:
60 + 2n + n2 = 21 + -21 + -2n + 2n + -1n2 + n2

Combine like terms: 21 + -21 = 0
60 + 2n + n2 = 0 + -2n + 2n + -1n2 + n2
60 + 2n + n2 = -2n + 2n + -1n2 + n2

Combine like terms: -2n + 2n = 0
60 + 2n + n2 = 0 + -1n2 + n2
60 + 2n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
60 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 2n + -60 + n2 = 0 + -60

Reorder the terms:
60 + -60 + 2n + n2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 2n + n2 = 0 + -60
2n + n2 = 0 + -60

Combine like terms: 0 + -60 = -60
2n + n2 = -60

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = -60 + 1

Reorder the terms:
1 + 2n + n2 = -60 + 1

Combine like terms: -60 + 1 = -59
1 + 2n + n2 = -59

Factor a perfect square on the left side:
(n + 1)(n + 1) = -59

Can't calculate square root of the right side.

The solution to this equation could not be determined.