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

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

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

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

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

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

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

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

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

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

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

Solving
8t + -16t2 = 0

Solving for variable 't'.

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}