-24z^2-42z-9=0

Solution for -24z^2-42z-9=0 equation:

Simplifying
-24z2 + -42z + -9 = 0

Reorder the terms:
-9 + -42z + -24z2 = 0

Solving
-9 + -42z + -24z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(3 + 14z + 8z2) = 0

Factor a trinomial.
-3((3 + 2z)(1 + 4z)) = 0

Ignore the factor -3.
Subproblem 1
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
Subproblem 2
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
Solution
z = {-1.5, -0.25}