solve z^3 + 2z^2 + 3z + 2 = 0?

Question

I attempted to factor this into:
z(z^2 + 3) + 2(z^2 + 2) = 0
but that didnt help because there were no common factors. 
My next attempt was to multiply the polynomial P(z) by various linear factors like z - 1, 1 - z, and even quadratic z^2 - z to manipulate into more simply solvable form but that was to no avail. I then tried putting all of the z's into re^ix form but that was a last resort. 
Ive seen the answer on wolfram as -1, 1/2(sqrt(7 +/- i) but i have no idea how to get that.

Anyone know how to do this?

TheSicilianSage · Accepted Answer

... z^3 + 2z^2 + 3z + 2 = 0
or z^3 + z^2 + z^2 + 2z + z + 2
or (z^3 + z^2 + 2z) + (z^2 + z + 2)
or (z) (z^2 + z + 2) + (z^2 + z + 2)
or (z + 1) (z^2 + z + 2)

Anonymous · Answer

You can factor it to (z^2+z+2)*(z+1)

The factors are then -1, -.5 + i*sqrt(7)/2, -.5 - i*sqrt(7)/2

Or.. -1, -.5 + 1.323i, -.5 - 1.323i

i is the imaginary number = sqrt(-1)

Hope this helps!

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solve z^3 + 2z^2 + 3z + 2 = 0?

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