When the object hits the ground, the value of h(t) of the given function becomes 0 such that,
0 = -16t² + 144 or 144 - 16t² = 0
The equation above becomes a difference of two squares where 144 is the square of 12 and 16t² if the square of 4t. Factoring then gives,
(12 - 4t) x (12 + 4t) = 0
12 - 4t = 0 ; t = 3 and 12 + 4t = 0 ; t = -3
The answer is 3 seconds.
