n^2-16n+57=-3

Solution for n^2-16n+57=-3 equation:

Simplifying
n2 + -16n + 57 = -3

Reorder the terms:
57 + -16n + n2 = -3

Solving
57 + -16n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
57 + 3 + -16n + n2 = -3 + 3

Combine like terms: 57 + 3 = 60
60 + -16n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
60 + -16n + n2 = 0

Factor a trinomial.
(6 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

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

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

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {6, 10}