4z^2-15z-234=0

Solution for 4z^2-15z-234=0 equation:

Simplifying
4z2 + -15z + -234 = 0

Reorder the terms:
-234 + -15z + 4z2 = 0

Solving
-234 + -15z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(39 + -4z) = 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 '(39 + -4z)' equal to zero and attempt to solve:

Simplifying
39 + -4z = 0

Solving
39 + -4z = 0

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

Add '-39' to each side of the equation.
39 + -39 + -4z = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -4z = 0 + -39
-4z = 0 + -39

Combine like terms: 0 + -39 = -39
-4z = -39

Divide each side by '-4'.
z = 9.75

Simplifying
z = 9.75
Solution
z = {-6, 9.75}