-p(p+2)(p-3)=0

Solution for -p(p+2)(p-3)=0 equation:

Simplifying
-1p(p + 2)(p + -3) = 0

Reorder the terms:
-1p(2 + p)(p + -3) = 0

Reorder the terms:
-1p(2 + p)(-3 + p) = 0

Multiply (2 + p) * (-3 + p)
-1p(2(-3 + p) + p(-3 + p)) = 0
-1p((-3 * 2 + p * 2) + p(-3 + p)) = 0
-1p((-6 + 2p) + p(-3 + p)) = 0
-1p(-6 + 2p + (-3 * p + p * p)) = 0
-1p(-6 + 2p + (-3p + p2)) = 0

Combine like terms: 2p + -3p = -1p
-1p(-6 + -1p + p2) = 0
(-6 * -1p + -1p * -1p + p2 * -1p) = 0
(6p + 1p2 + -1p3) = 0

Solving
6p + 1p2 + -1p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(6 + p + -1p2) = 0

Factor a trinomial.
p((3 + -1p)(2 + 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 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2
Solution
p = {0, 3, -2}