p^3-3p=0

Solution for p^3-3p=0 equation:

Simplifying
p3 + -3p = 0

Reorder the terms:
-3p + p3 = 0

Solving
-3p + p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-3 + p2) = 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 + p2)' equal to zero and attempt to solve:

Simplifying
-3 + p2 = 0

Solving
-3 + p2 = 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 + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + p2 = 0 + 3
p2 = 0 + 3

Combine like terms: 0 + 3 = 3
p2 = 3

Simplifying
p2 = 3

Take the square root of each side:
p = {-1.732050808, 1.732050808}
Solution
p = {0, -1.732050808, 1.732050808}