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Simplifying (6p + 17)(2p + 2) = 0 Reorder the terms: (17 + 6p)(2p + 2) = 0 Reorder the terms: (17 + 6p)(2 + 2p) = 0 Multiply (17 + 6p) * (2 + 2p) (17(2 + 2p) + 6p * (2 + 2p)) = 0 ((2 * 17 + 2p * 17) + 6p * (2 + 2p)) = 0 ((34 + 34p) + 6p * (2 + 2p)) = 0 (34 + 34p + (2 * 6p + 2p * 6p)) = 0 (34 + 34p + (12p + 12p2)) = 0 Combine like terms: 34p + 12p = 46p (34 + 46p + 12p2) = 0 Solving 34 + 46p + 12p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(17 + 23p + 6p2) = 0 Factor a trinomial. 2((17 + 6p)(1 + p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + 6p)' equal to zero and attempt to solve: Simplifying 17 + 6p = 0 Solving 17 + 6p = 0 Move all terms containing p to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 6p = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 6p = 0 + -17 6p = 0 + -17 Combine like terms: 0 + -17 = -17 6p = -17 Divide each side by '6'. p = -2.833333333 Simplifying p = -2.833333333Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 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 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Solution
p = {-2.833333333, -1}
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