12z^2-5z-2=0

Solution for 12z^2-5z-2=0 equation:

Simplifying
12z2 + -5z + -2 = 0

Reorder the terms:
-2 + -5z + 12z2 = 0

Solving
-2 + -5z + 12z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -4z)(2 + -3z) = 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 '(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 = {-0.25, 0.6666666667}