4z^2-23z-6=0

Solution for 4z^2-23z-6=0 equation:

Simplifying
4z2 + -23z + -6 = 0

Reorder the terms:
-6 + -23z + 4z2 = 0

Solving
-6 + -23z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -4z)(6 + -1z) = 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 '(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
Solution
z = {-0.25, 6}