Answer
$x=-2$; $x=0.5$; $x=3$;
Work Step by Step
We use a graphing calculator to graph the function $y=2x^3-3x^2-11x+6$.
From the graph we notice that the $x$-intercepts are:
$$\begin{align*}
x_1&=-2\\
x_2&=0.5\\
x_3&=3.
\end{align*}$$
We check if the values $x_1$, $x_2$ and $x_3$ check the equation $2x^3-3x^2-11x+6=0$:
$$\begin{align*}
x_1&=-2\\
2(-2)^3-3(-2)^2-11(-2)+6&\stackrel{?}{=}0\\
-16-12+22+6&\stackrel{?}{=}0\\
0&=0\checkmark\\\\
x_2&=0.5\\
2(0.5)^3-3(0.5)^2-11(0.5)+6&\stackrel{?}{=}0\\
0.25-0.75-5.5+6&\stackrel{?}{=}0\\
0&=0\checkmark\\\\
x_3&=3\\
2(3^3)-3(3^2)-11(3)+6&\stackrel{?}{=}0\\
54-27-33+6&\stackrel{?}{=}0\\
0&=0\checkmark
\end{align*}$$
Therefore the solutions of the equation are $-2$, $0.5$ and $3$.
