This question is very unclear as to what it wants for an answer, so I'd just like to check and see if my working is satisfactory.
The question:
Solve the equation if -2 is a root.
All I did with my working is replace x with -2.
Is this going to satisfy the question?
No!!!
"Solve" the equation means
find all x for which the equation is true
hence, you must use the clue given to find the remaining solutions.
"Solve" means "find the solutions".
One solution is
Clearly, this is zero if since these are two ways to write the same expression.
If we multiply this out,
The other roots are complex.
No, one of the roots is
and it's the only real root.
There are also two complex roots, which are the solution to the 2nd factor being zero.
If you are familiar with complex numbers, then you need to solve
Otherwise, you need to be aware that is the only real root
since there is no real solution to
since is the solution to that.