3p^2(2p+1)=0

Solution for 3p^2(2p+1)=0 equation:

Simplifying
3p2(2p + 1) = 0

Reorder the terms:
3p2(1 + 2p) = 0
(1 * 3p2 + 2p * 3p2) = 0
(3p2 + 6p3) = 0

Solving
3p2 + 6p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p2'.
3p2(1 + 2p) = 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 '(1 + 2p)' equal to zero and attempt to solve:

Simplifying
1 + 2p = 0

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

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

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

Divide each side by '2'.
p = -0.5

Simplifying
p = -0.5
Solution
p = {0, -0.5}