24t=-16t^2

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

Simplifying
24t = -16t2

Solving
24t = -16t2

Solving for variable 't'.

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

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

Ignore the factor 8.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
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
Solution
t = {0, -1.5}