18z^2-31z+6=0

Solution for 18z^2-31z+6=0 equation:

Simplifying
18z2 + -31z + 6 = 0

Reorder the terms:
6 + -31z + 18z2 = 0

Solving
6 + -31z + 18z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -9z)(3 + -2z) = 0

Subproblem 1
Set the factor '(2 + -9z)' equal to zero and attempt to solve:

Simplifying
2 + -9z = 0

Solving
2 + -9z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9z = 0 + -2
-9z = 0 + -2

Combine like terms: 0 + -2 = -2
-9z = -2

Divide each side by '-9'.
z = 0.2222222222

Simplifying
z = 0.2222222222
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {0.2222222222, 1.5}