0=2p^3-p^2-6p

Solution for 0=2p^3-p^2-6p equation:

Simplifying
0 = 2p3 + -1p2 + -6p

Reorder the terms:
0 = -6p + -1p2 + 2p3

Solving
0 = -6p + -1p2 + 2p3

Solving for variable 'p'.
Remove the zero:
6p + p2 + -2p3 = -6p + -1p2 + 2p3 + 6p + p2 + -2p3

Reorder the terms:
6p + p2 + -2p3 = -6p + 6p + -1p2 + p2 + 2p3 + -2p3

Combine like terms: -6p + 6p = 0
6p + p2 + -2p3 = 0 + -1p2 + p2 + 2p3 + -2p3
6p + p2 + -2p3 = -1p2 + p2 + 2p3 + -2p3

Combine like terms: -1p2 + p2 = 0
6p + p2 + -2p3 = 0 + 2p3 + -2p3
6p + p2 + -2p3 = 2p3 + -2p3

Combine like terms: 2p3 + -2p3 = 0
6p + p2 + -2p3 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(6 + p + -2p2) = 0

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

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

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

Simplifying
3 + 2p = 0

Solving
3 + 2p = 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 + 2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2p = 0 + -3
2p = 0 + -3

Combine like terms: 0 + -3 = -3
2p = -3

Divide each side by '2'.
p = -1.5

Simplifying
p = -1.5
Solution
p = {0, 2, -1.5}