Answer
$x=\left\{ 0,-\dfrac{3}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
6x^2+9x=0
,$ express the equation in factored form. Next step is to equate each factor to zero (Zero Product Property). Finally, solve each equation.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=3x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
3x(2x+3)=0
.\end{array}
Equating each factor to zero (Zero Product Property), the solutions to the equation above are
\begin{array}{l}\require{cancel}
3x=0
\\\\\text{OR}\\\\
2x+3=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x=0
\\\\
x=\dfrac{0}{3}
\\\\
x=0
\\\\\text{OR}\\\\
2x+3=0
\\\\
2x=-3
\\\\
x=-\dfrac{3}{2}
.\end{array}
Hence, $
x=\left\{ 0,-\dfrac{3}{2} \right\}
.$