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Simplifying (3p + 4)(2p + 5) = 0 Reorder the terms: (4 + 3p)(2p + 5) = 0 Reorder the terms: (4 + 3p)(5 + 2p) = 0 Multiply (4 + 3p) * (5 + 2p) (4(5 + 2p) + 3p * (5 + 2p)) = 0 ((5 * 4 + 2p * 4) + 3p * (5 + 2p)) = 0 ((20 + 8p) + 3p * (5 + 2p)) = 0 (20 + 8p + (5 * 3p + 2p * 3p)) = 0 (20 + 8p + (15p + 6p2)) = 0 Combine like terms: 8p + 15p = 23p (20 + 23p + 6p2) = 0 Solving 20 + 23p + 6p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + 2p)(4 + 3p) = 0Subproblem 1
Set the factor '(5 + 2p)' equal to zero and attempt to solve: Simplifying 5 + 2p = 0 Solving 5 + 2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2p = 0 + -5 2p = 0 + -5 Combine like terms: 0 + -5 = -5 2p = -5 Divide each side by '2'. p = -2.5 Simplifying p = -2.5Subproblem 2
Set the factor '(4 + 3p)' equal to zero and attempt to solve: Simplifying 4 + 3p = 0 Solving 4 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3p = 0 + -4 3p = 0 + -4 Combine like terms: 0 + -4 = -4 3p = -4 Divide each side by '3'. p = -1.333333333 Simplifying p = -1.333333333Solution
p = {-2.5, -1.333333333}
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