So since in this example we have 4 terms, we can use a cool method of factoring called grouping, where we cut the equation into two groups of two terms. So we got x3 + 10x2 + 9x + 90. Look at the first two terms, x3 and 10x2. We can pull out a gcf here of x2, getting us x2 (x+10). The same can be done with the last two terms, with a gcf of 9, getting us 9 (x+10). So, through this, we can take each gcf and group those as a term, being (x2 + 9). Then, since we have 2 of the term (x+10), we'll end up getting the same 2 answers when setting that equal to zero. If we set each factored term to zero now to solve for x, we end up with the -10 that you found on your calculator, and when we set x2 + 9=0, we can see that we'll end up getting 2 imaginary numbers because we end up taking the square root of a negative, which we don't worry about. So the answer is just x=-10.
Also, if you wanna check your work for yourself and see this work, if you have a graphing calculator, you can graph the original function and then look where the x coordinate of the graph equals 0, aka where the graph's x intercepts are, and those are also your answers. So I graphed this function and lo and behold, the only x intercept was at -10, meaning that's your only answer.