Strategy in solving quadratics

Esma and Hunter were trying to solve the equation:

They both agreed they should first subtract $2x$2, x and add $8$8 to both sides and rewrite the equation as $x^2+6x+8=0$x, squared, plus, 6, x, plus, 8, equals, 0.

Then Esma said, "I can complete the square. I can add $1$1 to both sides to rewrite this equation as $x^2+6x+9=1$x, squared, plus, 6, x, plus, 9, equals, 1, factor, and solve using square roots."

Hunter said, “I'll factor the left-hand side of the equation as $(x+2)(x+4)$left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 4, right parenthesis and solve using the zero product property.”