The formula h=48t-16t^2 gives the height h, in feet, of an object projected into the air after t seconds. If an object is propelled upward, at what times will it reach a height of 32 feet above the ground?

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 at 1 second and 2 seconds after launch.