The expression in x is always greater than or equal to zero (because x to an even power is never negative). Hence the limit -4 is irrelevant and we only need to consider the limit 21.
After subtracting 21, the expression can be factored as
... x⁴ +4x² -21 < 0
... (x²+7)(x²-3) < 0
... (x²+7)(x+√3)(x-√3) < 0 . . . . . factoring the difference of squares
The left factor is always positive, so the expression will be negative when one, but not both, of the factors involving √3 is negative. That happens when
... -√3 < x < √3
In interval notation: (-√3, √3).
