12z^2-5z-3=0

Solution for 12z^2-5z-3=0 equation:

Simplifying
12z2 + -5z + -3 = 0

Reorder the terms:
-3 + -5z + 12z2 = 0

Solving
-3 + -5z + 12z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-1 + -3z = 0

Solving
-1 + -3z = 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 + -3z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3z = 0 + 1
-3z = 0 + 1

Combine like terms: 0 + 1 = 1
-3z = 1

Divide each side by '-3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Subproblem 2
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
Solution
z = {-0.3333333333, 0.75}