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Simplifying 5p(3p + 4)(2p + 3) = 0 Reorder the terms: 5p(4 + 3p)(2p + 3) = 0 Reorder the terms: 5p(4 + 3p)(3 + 2p) = 0 Multiply (4 + 3p) * (3 + 2p) 5p(4(3 + 2p) + 3p * (3 + 2p)) = 0 5p((3 * 4 + 2p * 4) + 3p * (3 + 2p)) = 0 5p((12 + 8p) + 3p * (3 + 2p)) = 0 5p(12 + 8p + (3 * 3p + 2p * 3p)) = 0 5p(12 + 8p + (9p + 6p2)) = 0 Combine like terms: 8p + 9p = 17p 5p(12 + 17p + 6p2) = 0 (12 * 5p + 17p * 5p + 6p2 * 5p) = 0 (60p + 85p2 + 30p3) = 0 Solving 60p + 85p2 + 30p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p'. 5p(12 + 17p + 6p2) = 0 Factor a trinomial. 5p((3 + 2p)(4 + 3p)) = 0 Ignore the factor 5.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 = 0Subproblem 2
Set the factor '(3 + 2p)' equal to zero and attempt to solve: Simplifying 3 + 2p = 0 Solving 3 + 2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2p = 0 + -3 2p = 0 + -3 Combine like terms: 0 + -3 = -3 2p = -3 Divide each side by '2'. p = -1.5 Simplifying p = -1.5Subproblem 3
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 = {0, -1.5, -1.333333333}
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