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Can somebody tell me what to do next for solving polynomial equations?

x^3 - 3x^2 -4x + 12= 0

I got the factors of 12 and i used 2.

(x+2) (x^2 + x + 12)=0

What do I do next?

I used synthetic division to get (x+2)(x^2 + x + 12)=0

Factor x^2+x+12 now

(x+4)(x+3)=0
therefore, (x+2)(x+4)(x+3)=0?

x= -2, -4, -3?

(x+3)(x+5)

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