Answer
$2$ seconds and $3$ seconds
Work Step by Step
Substituting $h(t)=96,$ in $h(t)=-16t^2+80t,$ then
\begin{array}{l}\require{cancel}
96=-16t^2+80t
\\
16t^2-80t+96=0
\\
\dfrac{16t^2-80t+96}{16}=\dfrac{0}{16}
\\
t^2-5t+6=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(t-3)(t-2)=0
.\end{array}
Equating each factor to zero (Zero Product Property) then the solutions of the equation above are $
t=\{ 2,3 \}
.$ Hence, at $2$ seconds and $3$ seconds, the height of the rocket is $96$ feet.
