#### Answer

$x=\left\{ 1,\dfrac{5}{8} \right\}$

#### Work Step by Step

Equating each factor to zero (Zero Product Principle), then the solutions to the given equation, $
(5t-8)(t-1)=0
,$ is
\begin{array}{l}
5t-8=0
\\\\
5t=8
\\\\
t=\dfrac{8}{5}
,\\\\\text{OR}\\\\
t-1=0
\\\\
t=1
.\end{array}
Hence, $
x=\left\{ 1,\dfrac{5}{8} \right\}
.$