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

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

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

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

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

Multiply (-1 + 3p) * (-1 + 2p)
(-1(-1 + 2p) + 3p * (-1 + 2p)) = 0
((-1 * -1 + 2p * -1) + 3p * (-1 + 2p)) = 0
((1 + -2p) + 3p * (-1 + 2p)) = 0
(1 + -2p + (-1 * 3p + 2p * 3p)) = 0
(1 + -2p + (-3p + 6p2)) = 0

Combine like terms: -2p + -3p = -5p
(1 + -5p + 6p2) = 0

Solving
1 + -5p + 6p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(1 + -3p)(1 + -2p) = 0

Subproblem 1
Set the factor '(1 + -3p)' equal to zero and attempt to solve:

Simplifying
1 + -3p = 0

Solving
1 + -3p = 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 + -3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3p = 0 + -1
-3p = 0 + -1

Combine like terms: 0 + -1 = -1
-3p = -1

Divide each side by '-3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
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 = {0.3333333333, 0.5}