First factor out $\displaystyle-{16}\usepackage{cmbright}\Huge\$ : $\displaystyle-{16}{\left({{t}}^{{2}}-{16}\right)}={0}\usepackage{cmbright}\Huge\$

This is the difference of two squares, so factor and solve.

$\displaystyle{t}-{4}={0}\usepackage{cmbright}\Huge\$ or $\displaystyle{t}+{4}={0}\usepackage{cmbright}\Huge\$

$\displaystyle{t}={4}\usepackage{cmbright}\Huge\$ or $\displaystyle{t}=-{4}\usepackage{cmbright}\Huge\$

The object will hit the ground in 4 seconds. Since time cannot be negative, $\displaystyle-{4}\usepackage{cmbright}\Huge\$ is not a solution.