Question 132887
Given :
{{{h = -16t^2 + 112t + 128}}}

When the ball hits the ground, the value of h is 0. So

{{{0 = -16t^2 + 112t + 128}}}   divide through by 16
{{{0 = -t^2 + 7t + 8 }}}

factor the equation
{{{0 = (-t + 8)(t + 1)}}}

So, either -t+8 = 0  or (t+1) =0
possible answers are t = 8  and t = -1

Since t cannot be 'minus time', only t = 8 makes sense.

Answer t = 8 seconds

Verify the answer by plugging 8 into the original equation, solve and verify the result is 0.