8z^2-22z+12=0

Solution for 8z^2-22z+12=0 equation:

Simplifying
8z2 + -22z + 12 = 0

Reorder the terms:
12 + -22z + 8z2 = 0

Solving
12 + -22z + 8z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11z + 4z2) = 0

Factor a trinomial.
2((3 + -4z)(2 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {0.75, 2}