Expand the vertex form into standard quadratic form; then use the quadratic root formula to determine the roots.

##y=3(x+7)^2-2##

##=3(x^2+14x+49)-2##

##= 3x^2+42x+145##

Using the formula for determining roots (and a very sharp pencil) ##(-b+-sqrt(b^2-4ac))/(2a)##

gives roots at ##x= -7+sqrt(6)/3## and ##x= -7-sqrt(6)/3##

So ##x+7-sqrt(6)/3## and ##x+7+sqrt(6)/3## are factors of the original equation

Fully factored form ##y=3(x+7)^2-2##

##= 3(x+7-sqrt(6)/3)(x+7+sqrt(6)/3)##

Expand the vertex form into standard quadratic form; then use the quadratic root formula to determine the roots.

##y=3(x+7)^2-2##

##=3(x^2+14x+49)-2##

##= 3x^2+42x+145##

Using the formula for determining roots (and a very sharp pencil) ##(-b+-sqrt(b^2-4ac))/(2a)##

gives roots at ##x= -7+sqrt(6)/3## and ##x= -7-sqrt(6)/3##

So ##x+7-sqrt(6)/3## and ##x+7+sqrt(6)/3## are factors of the original equation

Fully factored form ##y=3(x+7)^2-2##

##= 3(x+7-sqrt(6)/3)(x+7+sqrt(6)/3)##