#### Answer

$x=\left\{ -\dfrac{9}{2},\dfrac{3}{4} \right\}$

#### Work Step by Step

Dividing both sides by $
6
,$ the given equation, $
6(4x-3)(2x+9)=0
,$ is equivalent to
\begin{array}{l}
(4x-3)(2x+9)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(4x-3)(2x+9)=0
,$ is
\begin{array}{l}
4x-3=0
\\\\
4x=3
\\\\
x=\dfrac{3}{4}
,\\\\\text{OR}\\\\
2x+9=0
\\\\
2x=-9
\\\\
x=-\dfrac{9}{2}
.\end{array}
Hence, $
x=\left\{ -\dfrac{9}{2},\dfrac{3}{4} \right\}
.$