how do I determine all solutions (real and non-real) for this?

Question

52.9(x + 8.62)(x^2 + 11)(x-46.3)^7 = 0

my teacher told me "set all equal to zero and solve for x" but I have no clue how to actually do that someone please help

Answer 1

A primary property of real numbers is that if AB=0, then either A=0 or B=0 (or both), where A and B are real numbers.

Therefore, in your problem,each of the factors can/must be set=0.

The constant multiplier divides out.

The first factor provides x=-8.62

The second factor provides x=±√11.

The third factor provides x=46.3 (because the only time x⁷=0 is when x=0.