Answer
The solutions are $x=\left\{-1, -0.25, 0.25\right\}$.
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Graph the functions $y=16x^3+16x^2$ (red graph) and $y=x+1$ (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 $16x^3+16x^2$ is equal tot he value of $y=x+1$ are equal..
The x-coordinates of these points are the solutions to the given equation.
Notice that the graphs intersect at the points $(-1, 0)$, $(-0.25, 0.75)$, and $(0.25, 1.25)$.
This means that the solutions to the given equation are $-1, -0.25, $ and $0.25$.
Thus, the solutions are $x=\left\{-1, -0.25, 0.25\right\}$.
