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.
(13 + r)(4 + r) = 0

Subproblem 1
Set the factor '(13 + r)' equal to zero and attempt to solve:

Simplifying
13 + r = 0

Solving
13 + r = 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 + r = 0 + -13

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

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

Simplifying
r = -13
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 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 + r = 0 + -4

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

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

Simplifying
r = -4
Solution
r = {-13, -4}