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Simplifying (7p + 7)(8 + 2p) = 0 Reorder the terms: (7 + 7p)(8 + 2p) = 0 Multiply (7 + 7p) * (8 + 2p) (7(8 + 2p) + 7p * (8 + 2p)) = 0 ((8 * 7 + 2p * 7) + 7p * (8 + 2p)) = 0 ((56 + 14p) + 7p * (8 + 2p)) = 0 (56 + 14p + (8 * 7p + 2p * 7p)) = 0 (56 + 14p + (56p + 14p2)) = 0 Combine like terms: 14p + 56p = 70p (56 + 70p + 14p2) = 0 Solving 56 + 70p + 14p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '14'. 14(4 + 5p + p2) = 0 Factor a trinomial. 14((4 + p)(1 + p)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Subproblem 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 = {-4, -1}
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