8z^2-54z+13=0

Solution for 8z^2-54z+13=0 equation:

Simplifying
8z2 + -54z + 13 = 0

Reorder the terms:
13 + -54z + 8z2 = 0

Solving
13 + -54z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -4z)(13 + -2z) = 0

Subproblem 1
Set the factor '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 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 + -4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4z = 0 + -1
-4z = 0 + -1

Combine like terms: 0 + -1 = -1
-4z = -1

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Subproblem 2
Set the factor '(13 + -2z)' equal to zero and attempt to solve:

Simplifying
13 + -2z = 0

Solving
13 + -2z = 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 + -2z = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2z = 0 + -13
-2z = 0 + -13

Combine like terms: 0 + -13 = -13
-2z = -13

Divide each side by '-2'.
z = 6.5

Simplifying
z = 6.5
Solution
z = {0.25, 6.5}