have I done the quadratic equation correctly?

[Gringo123]

x2 + 3x + 2 = 0

(x + 1) (x + 2)

so x = -1 or -2

Is that right?

[Mentallic]

Yes. You can check if you factorized correctly by expanding your factors out.
or... you can check if your answers are correct by substituting them into the quadratic.

If the left-hand side is equal to the right-hand side, then you've found the correct values for x.