Given

#color(white)("XXX")y=color(brown)((2x+1)(x+6))+6x#

(first converting into standard form):

#color(white)("XXX")rArr y=color(brown)(2x(x+6)+1(x+6))+6x#

#color(white)("XXX")rArr y =color(brown)( 2x^2+12x+x+6)+6x#

#color(white)("XXX")rArr y= 2x^2+19x+6#

Remember the vertex form is #y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)# with vertex at #(color(red)(a),color(blue)(b))#

Extract the #color(green)(m)# factor

#color(white)("XXX")y=color(green)(2)(x^2+19/2x)+6#

Complete the square

#color(white)("XXX")y=color(green)(2)(x^2+19/2x+(19/4)^2)+6-2*(19/4)^2#

Simplify into vertex form

#color(white)("XXX")y=color(green)(2)(x-(color(red)(-19/4)))^2+(color(blue)(-313/8))#

Since #-19/4# is about #-5#

and #-313/8# is about #-39#

the graph below of the original equation supports this answer.

graph{(2x+1)(x+6)+6x [-19.8, 12.24, -40.05, -24.01]}