z^2+17z+52=

Solution for z^2+17z+52= equation:

Simplifying
z2 + 17z + 52 = 0

Reorder the terms:
52 + 17z + z2 = 0

Solving
52 + 17z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
13 + z = 0

Solving
13 + z = 0

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

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

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

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

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

Simplifying
4 + z = 0

Solving
4 + z = 0

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

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

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

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

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