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Simplifying (7p + 7p3 + -7p3) + -1(8p3 + 2p + 6p2) = 0 Combine like terms: 7p3 + -7p3 = 0 (7p + 0) + -1(8p3 + 2p + 6p2) = 0 (7p) + -1(8p3 + 2p + 6p2) = 0 (7p) + -1(8p3 + 2p + 6p2) = 0 Reorder the terms: (7p) + -1(2p + 6p2 + 8p3) = 0 (7p) + (2p * -1 + 6p2 * -1 + 8p3 * -1) = 0 (7p) + (-2p + -6p2 + -8p3) = 0 Combine like terms: (7p) + -2p = 5p 5p + -6p2 + -8p3 = 0 Solving 5p + -6p2 + -8p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(5 + -6p + -8p2) = 0 Factor a trinomial. p((1 + -2p)(5 + 4p)) = 0Subproblem 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 '(1 + -2p)' equal to zero and attempt to solve: Simplifying 1 + -2p = 0 Solving 1 + -2p = 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 + -2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2p = 0 + -1 -2p = 0 + -1 Combine like terms: 0 + -1 = -1 -2p = -1 Divide each side by '-2'. p = 0.5 Simplifying p = 0.5Subproblem 3
Set the factor '(5 + 4p)' equal to zero and attempt to solve: Simplifying 5 + 4p = 0 Solving 5 + 4p = 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 + 4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4p = 0 + -5 4p = 0 + -5 Combine like terms: 0 + -5 = -5 4p = -5 Divide each side by '4'. p = -1.25 Simplifying p = -1.25Solution
p = {0, 0.5, -1.25}
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