We want to get it in the form



where the vertex is (h,k) and the axis of symmetry
is the vertical line whose equation is x=h.

Make sure it's in order of descending powers:



Factor out the coefficient of the first two terms.
It's 1 here so this step isn't necessary, but I'll
do it anyway so it'll be in the form 



1.  Multiply the coefficient of x, which is 6, by 1/2, getting 3.
2.  Square the result of step 1, 32=9
3.  Add and subtract that number, that is add + 9 - 9 after the 6x:



Factor the first three terms:



If you followed the 3 steps above both factors are the same and
it can be written as the square of a binomial:



Distribute to remove the outer (large) parentheses, leaving the
square of the binomial intact:



Combine the remaining terms as -10



That's in the form 



where a=1, -h=+3, i.e., h=-3, k=-10

so the vertex is (h,k) = (-3,-10) and the axis of symmetry
is the vertical line whose equation is x=h, or x=-3. 



Edwin