Factor.
Think of it has a normal quadratic equation with an x squared term, x term, and constant.
[tex](x^2+7)(x^2-4)=0[/tex]
[tex]x^2+7=0[/tex]
[tex]x^2=-7 [/tex]
[tex]x= \sqrt{-7} [/tex]
That won't give use any real roots.
[tex]x^2-4=0[/tex]
[tex]x^2=4[/tex]
[tex]x=-2,2[/tex]
So x = -2 and x = 2