Find the solution to the equation $\frac{x^{3}+10 x^{2}+25 x}{x+5}=0$

Step 1 ：The given equation is a rational function, which is \(\frac{x^{3}+10 x^{2}+25 x}{x+5}=0\).

Step 2 ：To solve it, we can set the numerator equal to zero, because a fraction is zero if and only if its numerator is zero. The denominator should not be zero because it would make the fraction undefined.

Step 3 ：So, we need to solve the equation \(x^{3}+10 x^{2}+25 x=0\) for x. This is a cubic equation and can be solved by factoring if possible.

Step 4 ：The solutions to the equation are x = -5 and x = 0.

Step 5 ：However, we need to check if these solutions make the original equation undefined. The original equation is undefined when the denominator is zero, i.e., x = -5.

Step 6 ：So, x = -5 is not a valid solution. The only valid solution is x = 0.

Step 7 ：Final Answer: The solution to the equation is \(\boxed{0}\).