n^2-20n+61=-3

Solution for n^2-20n+61=-3 equation:

Simplifying
n2 + -20n + 61 = -3

Reorder the terms:
61 + -20n + n2 = -3

Solving
61 + -20n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
61 + 3 + -20n + n2 = -3 + 3

Combine like terms: 61 + 3 = 64
64 + -20n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
64 + -20n + n2 = 0

Factor a trinomial.
(4 + -1n)(16 + -1n) = 0

Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Solution
n = {4, 16}