r^2-17r+52=0

Solution for r^2-17r+52=0 equation:

Simplifying
r2 + -17r + 52 = 0

Reorder the terms:
52 + -17r + r2 = 0

Solving
52 + -17r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + -1r)(13 + -1r) = 0

Subproblem 1
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
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 = {4, 13}