Answer
$t=\{-8,0,8\}$
Work Step by Step
First, subtract $t$ from both sides $$\frac{1}{64}t^3-t=0$$ Multiply both sides by $64$ to get $$t^3-64t=0$$ Both terms left of the equal sign have factor $t$, so factor out the $t$ to get $$t(t^2-64)=0$$ Using the fact that $a^2-b^2=(a-b)(a+b)$, the equation can be rewritten as $$t(t-8)(t+8)=0$$ Therefore, by setting each factor to zero, solutions are $$t=0$$ $$t-8=0 \implies t=8$$ $$t+8=0 \implies t=-8$$
