How to factor x^3+7x^2+15x+9=0

This is of the form ax^3+bx^2+cx+d=0. You will need to find all the factors of d, and see which make the equation true, or equal to zero ...

9=±1,3,9 (and also ±1/3, 1/9)

x=-3 makes the equation equal to zero so (x+3) is on factor.

Now you can divide the equation by (x+3) to find the other factors ...

(x^3+7x^2+15x+9) / (x+3)

x^2 remainder 4x^2+15x+9

4x remainder 3x+9

3 remainder 0 so

(x+3) (x^2+4x+3) now you can factor the term in the parentheses ...

(x+3) (x+1) (x+3) = 0

(x+1) (x+3) ^2=0 so x=-1, - 3