z^2-12z-13=0

Solution for z^2-12z-13=0 equation:

Simplifying
z2 + -12z + -13 = 0

Reorder the terms:
-13 + -12z + z2 = 0

Solving
-13 + -12z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1z = 0 + 1
-1z = 0 + 1

Combine like terms: 0 + 1 = 1
-1z = 1

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(13 + -1z)' equal to zero and attempt to solve:

Simplifying
13 + -1z = 0

Solving
13 + -1z = 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 + -1z = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1z = 0 + -13
-1z = 0 + -13

Combine like terms: 0 + -13 = -13
-1z = -13

Divide each side by '-1'.
z = 13

Simplifying
z = 13
Solution
z = {-1, 13}