You seem to want values of t that satisfy

32 = 48t - 16t^2

16t^2 - 48t + 32 = 0 (subtract the right side from both sides)

t^2 - 3t + 2 = 0 (divide by 16)

(t-1)(t-2) = 0 (factor)

t = 1 or t = 2 (recognize solutions will make the factors equal to zero)

The object will be 32 feet above the ground

32 = 48t - 16t^2

16t^2 - 48t + 32 = 0 (subtract the right side from both sides)

t^2 - 3t + 2 = 0 (divide by 16)

(t-1)(t-2) = 0 (factor)

t = 1 or t = 2 (recognize solutions will make the factors equal to zero)

The object will be 32 feet above the ground

**at 1 second and 2 seconds**after launch.