The given expression is,
[tex]x^3+14x^2+48x=0[/tex]Reordering the terms, we get,
[tex]48x+14x^2+x^3=0[/tex]Here, the GCF is x, therefore, we have,
[tex]\begin{gathered} x(48+14x+x^2)=0 \\ x((x+6)(x+8))=0 \end{gathered}[/tex]Equating each term to zero, we get,
[tex]\begin{gathered} x=0 \\ x=-6 \\ x=-8 \end{gathered}[/tex]Thus the solution is x = 0, -6, -8
