0=3p(2p-1)

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

Simplifying
0 = 3p(2p + -1)

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

Solving
0 = -3p + 6p2

Solving for variable 'p'.
Remove the zero:
3p + -6p2 = -3p + 6p2 + 3p + -6p2

Reorder the terms:
3p + -6p2 = -3p + 3p + 6p2 + -6p2

Combine like terms: -3p + 3p = 0
3p + -6p2 = 0 + 6p2 + -6p2
3p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
3p + -6p2 = 0

Factor out the Greatest Common Factor (GCF), '3p'.
3p(1 + -2p) = 0

Ignore the factor 3.
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 + -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}