24z^2-5z-1=0

Solution for 24z^2-5z-1=0 equation:

Simplifying
24z2 + -5z + -1 = 0

Reorder the terms:
-1 + -5z + 24z2 = 0

Solving
-1 + -5z + 24z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -8z)(1 + -3z) = 0

Subproblem 1
Set the factor '(-1 + -8z)' equal to zero and attempt to solve:

Simplifying
-1 + -8z = 0

Solving
-1 + -8z = 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 + -8z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8z = 0 + 1
-8z = 0 + 1

Combine like terms: 0 + 1 = 1
-8z = 1

Divide each side by '-8'.
z = -0.125

Simplifying
z = -0.125
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {-0.125, 0.3333333333}