24t^2-5t-1=0

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

Simplifying
24t2 + -5t + -1 = 0

Reorder the terms:
-1 + -5t + 24t2 = 0

Solving
-1 + -5t + 24t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(-1 + -8t)' equal to zero and attempt to solve:

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8t = 0 + 1

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

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

Divide each side by '-8'.
t = -0.125

Simplifying
t = -0.125
Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3t = 0 + -1

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

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

Divide each side by '-3'.
t = 0.3333333333

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