Bunuel
If you substitute x=-2 the equation will NOT hold true. Also, note that ALL numbers used on the GMAT are real numbers.
Hope it helps.
If you substitute x=-2. It becomes
LHS = -2
RHS = 4th root (-8+24) = 4th root (16) = +/-2 (because in the question it is not mentioned that x is only +ve)
So, equality holds true for x=-2.
In the solutions in each of the posts it is mentioned that \sqrt{expression} >=0, which is not true.
Square root of a number can be +/- a number.
Similarly 4th root of a number can be +ve or -ve.
But, 4th power of a number will always be +ve.
So, in the expression in question.
X can be + or -. But, (x^3 + 6x^2) should always be greater than or equal to 0.
16 = (2)^4
or
16 = (-2)^4