3p[2p(p+4)-p^2]=

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Solution for 3p[2p(p+4)-p^2]= equation: 


Simplifying
3p[2p(p + 4) + -1p2] = 0

Reorder the terms:
3p[2p(4 + p) + -1p2] = 0
3p[(4 * 2p + p * 2p) + -1p2] = 0
3p[(8p + 2p2) + -1p2] = 0

Combine like terms: 2p2 + -1p2 = 1p2
3p[8p + 1p2] = 0
[8p * 3p + 1p2 * 3p] = 0
[24p2 + 3p3] = 0

Solving
24p2 + 3p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p2'.
3p2(8 + p) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

Take the square root of each side:
p = {0}

Subproblem 2
Set the factor '(8 + p)' equal to zero and attempt to solve:

Simplifying
8 + p = 0

Solving
8 + p = 0

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

Add '-8' to each side of the equation.
8 + -8 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
Solution
p = {0, -8}

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