For zeroth order reaction,

    $\left[{\mathrm{A}}_{\mathrm{t}}\right]=\left[{\mathrm{A}}_0\right]-\mathrm{Kt}$

where, $\left[{\mathrm{A}}_{\mathrm{t}}\right]$$=$concentration after time $\mathrm{t}$     

              $\left[{\mathrm{A}}_0\right]$$=$initial concentration     

               $\mathrm{K}$$=$rate constant

                $\mathrm{t}$$=$time

At half life, $\left[{\mathrm{A}}_{\mathrm{t}}\right] =\frac{\left[{\mathrm{A}}_0\right]}{2}$

                    $$\begin{gathered} \frac{\left[{\mathrm{A}}_0\right]}{2}= \left[{\mathrm{A}}_0\right] - {\mathrm{Kt}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \\ {\mathrm{Kt}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right. }= \frac{\left[{\mathrm{A}}_0\right]}{2} \\ {\mathrm{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} = \frac{\left[{\mathrm{A}}_0\right]}{2 \mathrm{K}} \end{gathered}$$