12z^2-14z+4=0

Solution for 12z^2-14z+4=0 equation:

Simplifying
12z2 + -14z + 4 = 0

Reorder the terms:
4 + -14z + 12z2 = 0

Solving
4 + -14z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -7z + 6z2) = 0

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

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

Simplifying
2 + -3z = 0

Solving
2 + -3z = 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 + -3z = 0 + -2

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

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

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {0.5, 0.6666666667}