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)

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

Solving for variable 't'.

Combine like terms: 24 + 24 = 48
48 + 8t + -16t2 = -24 + -8t + 16t2 + 24 + 8t + -16t2

Reorder the terms:
48 + 8t + -16t2 = -24 + 24 + -8t + 8t + 16t2 + -16t2

Combine like terms: -24 + 24 = 0
48 + 8t + -16t2 = 0 + -8t + 8t + 16t2 + -16t2
48 + 8t + -16t2 = -8t + 8t + 16t2 + -16t2

Combine like terms: -8t + 8t = 0
48 + 8t + -16t2 = 0 + 16t2 + -16t2
48 + 8t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
48 + 8t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + t + -2t2) = 0

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

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
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 = {2, -1.5}