Answer
$$\{-5,2\}$$
Work Step by Step
Bring the equation to the standard form by moving all terms on one side:
$$\begin{align*}
(2x-3)(x+2)-x^2+2x-4&=0\\
2x^2+4x-3x-6-x^2+2x-4&=0\\
x^2+3x-10&=0.
\end{align*}$$
Factor the left side and determine the solutions:
$$\begin{align*}
(x-2)(x+5)&=0\\
x-2=0&\text{ or }x+5=0\\
x=2&\text{ or }x=-5.
\end{align*}$$
The solution set of the equation is:
$$\{-5,2\}.$$
