24=-16(t+-1.5)(t+1)

Solution for 24=-16(t+-1.5)(t+1) equation:

Simplifying
24 = -16(t + -1.5)(t + 1)

Reorder the terms:
24 = -16(-1.5 + t)(t + 1)

Reorder the terms:
24 = -16(-1.5 + t)(1 + t)

Multiply (-1.5 + t) * (1 + t)
24 = -16(-1.5(1 + t) + t(1 + t))
24 = -16((1 * -1.5 + t * -1.5) + t(1 + t))
24 = -16((-1.5 + -1.5t) + t(1 + t))
24 = -16(-1.5 + -1.5t + (1 * t + t * t))
24 = -16(-1.5 + -1.5t + (1t + t2))

Combine like terms: -1.5t + 1t = -0.5t
24 = -16(-1.5 + -0.5t + t2)
24 = (-1.5 * -16 + -0.5t * -16 + t2 * -16)
24 = (24 + 8t + -16t2)

Add '-24' to each side of the equation.
24 + -24 = 24 + 8t + -24 + -16t2

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

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

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

Solving
0 = 8t + -16t2

Solving for variable 't'.
Remove the zero:
-8t + 16t2 = 8t + -16t2 + -8t + 16t2

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

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

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

Factor out the Greatest Common Factor (GCF), '8t'.
8t(-1 + 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 '(-1 + 2t)' equal to zero and attempt to solve:

Simplifying
-1 + 2t = 0

Solving
-1 + 2t = 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 + 2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2t = 0 + 1
2t = 0 + 1

Combine like terms: 0 + 1 = 1
2t = 1

Divide each side by '2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {0, 0.5}