0=16t^2-8t-24

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

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

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

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

Solving for variable 't'.

Combine like terms: 0 + 24 = 24
24 + 8t + -16t2 = -24 + -8t + 16t2 + 24 + 8t + -16t2

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

Combine like terms: -24 + 24 = 0
24 + 8t + -16t2 = 0 + -8t + 8t + 16t2 + -16t2
24 + 8t + -16t2 = -8t + 8t + 16t2 + -16t2

Combine like terms: -8t + 8t = 0
24 + 8t + -16t2 = 0 + 16t2 + -16t2
24 + 8t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
24 + 8t + -16t2 = 0

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

Factor a trinomial.
8((3 + -2t)(1 + t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Solution
t = {1.5, -1}