$x=-6 \text{ or } x=-8$
$x= 6 \text{ or } x= -8$
$x= 6 \text{ or } x= 8$
$x= -6 \text{ or } x= 8$

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$\begin{aligned} x^2 + 14x + 48 & = 0\\ x^2 + 6x + 8x + 48 & = 0\\ x(x + 6) + 8(x + 6) & = 0\\ (x + 6)(x + 8) & = 0\\ (x + 6) = 0 \ \text{or} \ (x + 8) = 0\\ x \in \boxed{\{-6,-8\}} \end{aligned}$