2z^2-27z+13=0

Solution for 2z^2-27z+13=0 equation:

Simplifying
2z2 + -27z + 13 = 0

Reorder the terms:
13 + -27z + 2z2 = 0

Solving
13 + -27z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -2z)(13 + -1z) = 0

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
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 = {0.5, 13}