n^2-16n+31=3

Solution for n^2-16n+31=3 equation:

Simplifying
n2 + -16n + 31 = 3

Reorder the terms:
31 + -16n + n2 = 3

Solving
31 + -16n + n2 = 3

Solving for variable 'n'.

Reorder the terms:
31 + -3 + -16n + n2 = 3 + -3

Combine like terms: 31 + -3 = 28
28 + -16n + n2 = 3 + -3

Combine like terms: 3 + -3 = 0
28 + -16n + n2 = 0

Factor a trinomial.
(2 + -1n)(14 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {2, 14}