#### Answer

$x=\left\{ \dfrac{1}{7},\dfrac{3}{10} \right\}$

#### Work Step by Step

Dividing both sides by $
4
,$ the given equation, $
4(7x-1)(10x-3)=0
,$ is equivalent to
\begin{array}{l}
(7x-1)(10x-3)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(7x-1)(10x-3)=0
,$ is
\begin{array}{l}
7x-1=0
\\\\
7x=1
\\\\
x=\dfrac{1}{7}
,\\\\\text{OR}\\\\
10x-3=0
\\\\
10x=3
\\\\
x=\dfrac{3}{10}
.\end{array}
Hence, $
x=\left\{ \dfrac{1}{7},\dfrac{3}{10} \right\}
.$