#### Answer

$x=\left\{ -3,\dfrac{5}{2} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2x^2+x-15=0
,$ express the left side in factored form and equate each to factor to zero (Zero Product Property). Then use the properties of equality to isolate the variable in each equation.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of the equation above is
\begin{array}{l}\require{cancel}
(2x-5)(x+3)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
2x-5=0
\\\\\text{OR}\\\\
x+3=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-5=0
\\\\
2x=5
\\\\
x=\dfrac{5}{2}
\\\\\text{OR}\\\\
x+3=0
\\\\
x=-3
.\end{array}
Hence, the solutions are $
x=\left\{ -3,\dfrac{5}{2} \right\}
.$