p^3-9p=

Solution for p^3-9p= equation:

Simplifying
p3 + -9p = 0

Reorder the terms:
-9p + p3 = 0

Solving
-9p + p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-9 + p2) = 0

Factor a difference between two squares.
p((3 + p)(-3 + p)) = 0

Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

Move all terms containing p to the left, all other terms to the right.

Simplifying
p = 0
Subproblem 2
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 3
Set the factor '(-3 + p)' equal to zero and attempt to solve:

Simplifying
-3 + p = 0

Solving
-3 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + p = 0 + 3
p = 0 + 3

Combine like terms: 0 + 3 = 3
p = 3

Simplifying
p = 3
Solution
p = {0, -3, 3}