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

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

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

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

Multiply p2 * p
p3 + -1(2p) + (2p)(2p)(2p) = 0

Remove parenthesis around (2p)
p3 + -1 * 2p + (2p)(2p)(2p) = 0

Multiply -1 * 2
p3 + -2p + (2p)(2p)(2p) = 0

Remove parenthesis around (2p)
p3 + -2p + 2p(2p)(2p) = 0

Remove parenthesis around (2p)
p3 + -2p + 2p * 2p(2p) = 0

Remove parenthesis around (2p)
p3 + -2p + 2p * 2p * 2p = 0

Reorder the terms for easier multiplication:
p3 + -2p + 2 * 2 * 2p * p * p = 0

Multiply 2 * 2
p3 + -2p + 4 * 2p * p * p = 0

Multiply 4 * 2
p3 + -2p + 8p * p * p = 0

Multiply p * p
p3 + -2p + 8p2 * p = 0

Multiply p2 * p
p3 + -2p + 8p3 = 0

Reorder the terms:
-2p + p3 + 8p3 = 0

Combine like terms: p3 + 8p3 = 9p3
-2p + 9p3 = 0

Solving
-2p + 9p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-2 + 9p2) = 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 + 9p2)' equal to zero and attempt to solve:

Simplifying
-2 + 9p2 = 0

Solving
-2 + 9p2 = 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 + 9p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9p2 = 0 + 2
9p2 = 0 + 2

Combine like terms: 0 + 2 = 2
9p2 = 2

Divide each side by '9'.
p2 = 0.2222222222

Simplifying
p2 = 0.2222222222

Take the square root of each side:
p = {-0.471404521, 0.471404521}
Solution
p = {0, -0.471404521, 0.471404521}