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Simplifying 8p3 + 6p2 + -9p = 0 Reorder the terms: -9p + 6p2 + 8p3 = 0 Solving -9p + 6p2 + 8p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-9 + 6p + 8p2) = 0 Factor a trinomial. p((-3 + -2p)(3 + -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 '(-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 '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 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 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Solution
p = {0, -1.5, 0.75}
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