Answer
$\left\{-\dfrac{3}{2},\dfrac{5}{3}\right\}$
Work Step by Step
Using factoring of trinomials, the given equation, $
6x^2-x-15=0
,$ is equivalent to
\begin{align*}
(2x+3)(3x-5)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
2x+3=0 & 3x-5=0
\\
2x=-3 & 3x=5
\\\\
x=-\dfrac{3}{2} & x=\dfrac{5}{3}
.\end{array}
Hence, the solution set of the equation $
6x^2-x-15
$ is $\left\{-\dfrac{3}{2},\dfrac{5}{3}\right\}$.
