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Simplifying 4p3 + -30p2 + -16p = 0 Reorder the terms: -16p + -30p2 + 4p3 = 0 Solving -16p + -30p2 + 4p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2p'. 2p(-8 + -15p + 2p2) = 0 Factor a trinomial. 2p((-1 + -2p)(8 + -1p)) = 0 Ignore the factor 2.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 '(-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 '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {0, -0.5, 8}
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