Given the functions $f(x)$ and $g(x)$ below, find all solutions to the equation $f(x)=g(x)$ to the nearest hundredth. \[ \begin{array}{c} f(x)=0.2 x^{3}-1.5 x^{2}-0.2 x+5.6 \\ g(x)=-1.3|x|+4 \end{array} \]

Step 1 ：Given the functions $f(x)$ and $g(x)$ below, find all solutions to the equation $f(x)=g(x)$ to the nearest hundredth.

Step 2 ：\[\begin{array}{c}f(x)=0.2 x^{3}-1.5 x^{2}-0.2 x+5.6 \g(x)=-1.3|x|+4\end{array}\]

Step 3 ：The question is asking for the x-values where the two functions intersect. This means we need to set the two functions equal to each other and solve for x. However, the function g(x) is an absolute value function, which means it will split into two cases: one for x >= 0 and one for x < 0. We will need to solve the equation for both cases.

Step 4 ：For x >= 0, the solutions are \(-0.71, 1.75, 6.46\).

Step 5 ：For x < 0, the solutions are \(-1.45, 0.66, 8.29\).

Step 6 ：Final Answer: The solutions to the equation $f(x)=g(x)$ are \(\boxed{-1.45}\), \(\boxed{-0.71}\), \(\boxed{0.66}\), \(\boxed{1.75}\), and \(\boxed{6.46}\).