How do I go about finding the roots (real and complex) of this polynomial:

2x^3 + 7x^2 + 14x + 12

try x = ±1,±2,±3 ...

f(1) ≠0
f(-1) ≠0
...
I could not find any zeros with integer values of x,
so I tried some possible fractions and found
x = -3/2 to work

so it factors to (2x+3)((x^2 + 2x + 4) after a long division
so x = -3/2 or x = -1 ± i√3