2p^3=2p(p+2)

Solution for 2p^3=2p(p+2) equation:

Simplifying
2p3 = 2p(p + 2)

Reorder the terms:
2p3 = 2p(2 + p)
2p3 = (2 * 2p + p * 2p)
2p3 = (4p + 2p2)

Solving
2p3 = 4p + 2p2

Solving for variable 'p'.

Reorder the terms:
-4p + -2p2 + 2p3 = 4p + 2p2 + -4p + -2p2

Reorder the terms:
-4p + -2p2 + 2p3 = 4p + -4p + 2p2 + -2p2

Combine like terms: 4p + -4p = 0
-4p + -2p2 + 2p3 = 0 + 2p2 + -2p2
-4p + -2p2 + 2p3 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-4p + -2p2 + 2p3 = 0

Factor out the Greatest Common Factor (GCF), '2p'.
2p(-2 + -1p + p2) = 0

Factor a trinomial.
2p((-1 + -1p)(2 + -1p)) = 0

Ignore the factor 2.
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 '(-1 + -1p)' equal to zero and attempt to solve:

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1p = 0 + 1

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

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

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

Simplifying
p = -1
Subproblem 3
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
Solution
p = {0, -1, 2}