n^2-16n+19=4

Solution for n^2-16n+19=4 equation:

Simplifying
n2 + -16n + 19 = 4

Reorder the terms:
19 + -16n + n2 = 4

Solving
19 + -16n + n2 = 4

Solving for variable 'n'.

Reorder the terms:
19 + -4 + -16n + n2 = 4 + -4

Combine like terms: 19 + -4 = 15
15 + -16n + n2 = 4 + -4

Combine like terms: 4 + -4 = 0
15 + -16n + n2 = 0

Factor a trinomial.
(1 + -1n)(15 + -1n) = 0

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {1, 15}