k^2+17k+52=0

Solution for k^2+17k+52=0 equation:

Simplifying
k2 + 17k + 52 = 0

Reorder the terms:
52 + 17k + k2 = 0

Solving
52 + 17k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(13 + k)(4 + k) = 0

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

Simplifying
13 + k = 0

Solving
13 + k = 0

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

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

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

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

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

Simplifying
4 + k = 0

Solving
4 + k = 0

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

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

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

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

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