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

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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}

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