3z^2-14z-192=0

Solution for 3z^2-14z-192=0 equation:

Simplifying
3z2 + -14z + -192 = 0

Reorder the terms:
-192 + -14z + 3z2 = 0

Solving
-192 + -14z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(32 + -3z) = 0

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

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(32 + -3z)' equal to zero and attempt to solve:

Simplifying
32 + -3z = 0

Solving
32 + -3z = 0

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

Add '-32' to each side of the equation.
32 + -32 + -3z = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -3z = 0 + -32
-3z = 0 + -32

Combine like terms: 0 + -32 = -32
-3z = -32

Divide each side by '-3'.
z = 10.66666667

Simplifying
z = 10.66666667
Solution
z = {-6, 10.66666667}