0=-16(t-1.5)(t+1)

Solution for 0=-16(t-1.5)(t+1) equation:

Simplifying
0 = -16(t + -1.5)(t + 1)

Reorder the terms:
0 = -16(-1.5 + t)(t + 1)

Reorder the terms:
0 = -16(-1.5 + t)(1 + t)

Multiply (-1.5 + t) * (1 + t)
0 = -16(-1.5(1 + t) + t(1 + t))
0 = -16((1 * -1.5 + t * -1.5) + t(1 + t))
0 = -16((-1.5 + -1.5t) + t(1 + t))
0 = -16(-1.5 + -1.5t + (1 * t + t * t))
0 = -16(-1.5 + -1.5t + (1t + t2))

Combine like terms: -1.5t + 1t = -0.5t
0 = -16(-1.5 + -0.5t + t2)
0 = (-1.5 * -16 + -0.5t * -16 + t2 * -16)
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 + -1t + 2t2) = 0

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

Ignore the factor 8.
Subproblem 1
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
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 = {-1, 1.5}