z^2+26z+169=0

Solution for z^2+26z+169=0 equation:

Simplifying
z2 + 26z + 169 = 0

Reorder the terms:
169 + 26z + z2 = 0

Solving
169 + 26z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(13 + z)(13 + 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 '(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
Solution
z = {-13, -13}