n^2-16n+52=-3

Solution for n^2-16n+52=-3 equation:

Simplifying
n2 + -16n + 52 = -3

Reorder the terms:
52 + -16n + n2 = -3

Solving
52 + -16n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
52 + 3 + -16n + n2 = -3 + 3

Combine like terms: 52 + 3 = 55
55 + -16n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
55 + -16n + n2 = 0

Factor a trinomial.
(5 + -1n)(11 + -1n) = 0

Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
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 = {5, 11}