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 = -2.5t
24 = -16(1.5 + -2.5t + t2)
24 = (1.5 * -16 + -2.5t * -16 + t2 * -16)
24 = (-24 + 40t + -16t2)

Solving
24 = -24 + 40t + -16t2

Solving for variable 't'.

Combine like terms: 24 + 24 = 48
48 + -40t + 16t2 = -24 + 40t + -16t2 + 24 + -40t + 16t2

Reorder the terms:
48 + -40t + 16t2 = -24 + 24 + 40t + -40t + -16t2 + 16t2

Combine like terms: -24 + 24 = 0
48 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2
48 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2

Combine like terms: 40t + -40t = 0
48 + -40t + 16t2 = 0 + -16t2 + 16t2
48 + -40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
48 + -40t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + -5t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(6 + -5t + 2t2)' equal to zero and attempt to solve:

Simplifying
6 + -5t + 2t2 = 0

Solving
6 + -5t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
3 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2.5t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -2.5t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2.5t + t2 = 0 + -3
-2.5t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2.5t + t2 = -3

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -3 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -3 + 1.5625

Combine like terms: -3 + 1.5625 = -1.4375
1.5625 + -2.5t + t2 = -1.4375

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.