Answer
$x=\left\{-2.06, 0, 1.055\right\}$.
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Graph the functions $y=x(x-1)(x+2)$ (red graph) and $y=\frac{1}{6}x$ (blue graph) using a graphing utility. Refer to the image below for the graph.
(2) Identify the point/s where the graphs intersect each other. These are the points where the value of $x(x-1)(x+2)$ and $\frac{1}{6}x$ are equal.
The x-coordinates of these points are the solutions to the given equation.
Notice that the graphs intersect each other at $(-2.055, -0.342), (0,0),$ and $(1.055, 0.176)$.
This means that the solutions to the given equation are: $-2.055, 0,$, and $1.055$.
Thus, the solutions, rounded to two decimal places when needed, are:
$x=\left\{-2.06, 0, 1.055\right\}$.
