z^2-13z+12=0

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

Simplifying
z2 + -13z + 12 = 0

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

Solving
12 + -13z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -1z)(12 + -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 '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {1, 12}