r^2-16r+39=0

Solution for r^2-16r+39=0 equation:

Simplifying
r2 + -16r + 39 = 0

Reorder the terms:
39 + -16r + r2 = 0

Solving
39 + -16r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(13 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(13 + -1r)' equal to zero and attempt to solve:

Simplifying
13 + -1r = 0

Solving
13 + -1r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1r = 0 + -13
-1r = 0 + -13

Combine like terms: 0 + -13 = -13
-1r = -13

Divide each side by '-1'.
r = 13

Simplifying
r = 13
Solution
r = {3, 13}