6z^2-19z-172=0

Solution for 6z^2-19z-172=0 equation:

Simplifying
6z2 + -19z + -172 = 0

Reorder the terms:
-172 + -19z + 6z2 = 0

Solving
-172 + -19z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(43 + -6z) = 0

Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(43 + -6z)' equal to zero and attempt to solve:

Simplifying
43 + -6z = 0

Solving
43 + -6z = 0

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

Add '-43' to each side of the equation.
43 + -43 + -6z = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -6z = 0 + -43
-6z = 0 + -43

Combine like terms: 0 + -43 = -43
-6z = -43

Divide each side by '-6'.
z = 7.166666667

Simplifying
z = 7.166666667
Solution
z = {-4, 7.166666667}