Answer
$x=\left\{ -4,-\dfrac{3}{2},1 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x-1)(2x+3)(x+4)=0
,$ equate each factor to zero (Zero Product Property). Then solve each resulting equation.
$\bf{\text{Solution Details:}}$
Equating each factor to zero (Zero Product Property), the solutions of the equation above are
\begin{array}{l}\require{cancel}
x-1=0
\\\\\text{OR}\\\\
2x+3=0
\\\\\text{OR}\\\\
x+4=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x-1=0
\\\\
x=1
\\\\\text{OR}\\\\
2x+3=0
\\\\
2x=-3
\\\\
x=-\dfrac{3}{2}
\\\\\text{OR}\\\\
x+4=0
\\\\
x=-4
.\end{array}
Hence, the solutions are $
x=\left\{ -4,-\dfrac{3}{2},1 \right\}
.$