12z^2-4z-21=0

Solution for 12z^2-4z-21=0 equation:

Simplifying
12z2 + -4z + -21 = 0

Reorder the terms:
-21 + -4z + 12z2 = 0

Solving
-21 + -4z + 12z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -6z)(3 + -2z) = 0

Subproblem 1
Set the factor '(-7 + -6z)' equal to zero and attempt to solve:

Simplifying
-7 + -6z = 0

Solving
-7 + -6z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6z = 0 + 7
-6z = 0 + 7

Combine like terms: 0 + 7 = 7
-6z = 7

Divide each side by '-6'.
z = -1.166666667

Simplifying
z = -1.166666667
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 = {-1.166666667, 1.5}