We have solved the initial value problem for the displacement function $x(t)$ and found its derivative. Substituting the constant values we found results in the following.

$x(t)=-e^{-4t}6t{e}^{-4t}$

$x^{\text{'}}(t)=4e^{-4t}-24t{e}^{-4t}6e^{-4t}$

$=10e^{-4t}-24t{e}^{-4t}$

Now we must determine the time $($in s$)$ at which the mass passes through the equilibrium point, or in other words the value of $t$ such that $x(t)=0.$

$0=-e^{-4t}6t{e}^{-4t}$

$e^{-4t}=6t{e}^{-4t}$

$t=$