p3-16p=0

Factor p out of p3-16p.

Factor p out of p3.

p⋅p2-16p=0

Factor p out of -16p.

p⋅p2+p⋅-16=0

Factor p out of p⋅p2+p⋅-16.

p(p2-16)=0

p(p2-16)=0

Rewrite 16 as 42.

p(p2-42)=0

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=p and b=4.

p((p+4)(p-4))=0

Remove unnecessary parentheses.

p(p+4)(p-4)=0

p(p+4)(p-4)=0

p(p+4)(p-4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

p=0

p+4=0

p-4=0

Set the first factor equal to 0.

p=0

Set the next factor equal to 0.

p+4=0

Subtract 4 from both sides of the equation.

p=-4

p=-4

Set the next factor equal to 0.

p-4=0

Add 4 to both sides of the equation.

p=4

p=4

The final solution is all the values that make p(p+4)(p-4)=0 true.

p=0,-4,4

Solve for p p^3-16p=0