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Simplifying (3p + -1)(4p + 1) = 0 Reorder the terms: (-1 + 3p)(4p + 1) = 0 Reorder the terms: (-1 + 3p)(1 + 4p) = 0 Multiply (-1 + 3p) * (1 + 4p) (-1(1 + 4p) + 3p * (1 + 4p)) = 0 ((1 * -1 + 4p * -1) + 3p * (1 + 4p)) = 0 ((-1 + -4p) + 3p * (1 + 4p)) = 0 (-1 + -4p + (1 * 3p + 4p * 3p)) = 0 (-1 + -4p + (3p + 12p2)) = 0 Combine like terms: -4p + 3p = -1p (-1 + -1p + 12p2) = 0 Solving -1 + -1p + 12p2 = 0 Solving for variable 'p'. Factor a trinomial. (-1 + -4p)(1 + -3p) = 0Subproblem 1
Set the factor '(-1 + -4p)' equal to zero and attempt to solve: Simplifying -1 + -4p = 0 Solving -1 + -4p = 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 + -4p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4p = 0 + 1 -4p = 0 + 1 Combine like terms: 0 + 1 = 1 -4p = 1 Divide each side by '-4'. p = -0.25 Simplifying p = -0.25Subproblem 2
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 = 0.3333333333Solution
p = {-0.25, 0.3333333333}
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