5x(x+6)(x²-1)³

Write as a product of binomials

5x(x+6)(x²-1)(x²-1)(x²-1)

Now factor the last three factors

5x(x+6)(x-1)(x+1)(x-1)(x+1)(x-1)(x+1)

Set that = 0 

5x(x+6)(x-1)(x+1)(x-1)(x+1)(x-1)(x+1) = 0

and use the zero-factor property:

5x=0; x+6=0; x-1=0; x+1=0; x-1=0; x+1=0; x-1=0; x+1=0; 
 x=0;  x=-6;  x=1;   x=-1;  x=1;   x=-1;  x=1;   x=-1

0 is a zero only 1 time, so it has multiplicity 1.
-6 is a zero only 1 time, so it has multiplicity 1.
1 is a zero 3 times, so it has multiplicity 3.
-1 is a zero 3 times, so it has multiplicity 3.   
  
Edwin