24t^2-16t-8=0

Solution for 24t^2-16t-8=0 equation:

Simplifying
24t2 + -16t + -8 = 0

Reorder the terms:
-8 + -16t + 24t2 = 0

Solving
-8 + -16t + 24t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + -2t + 3t2) = 0

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

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-0.3333333333, 1}