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Simplifying 8p3 + -18p2 + 9p = 0 Reorder the terms: 9p + -18p2 + 8p3 = 0 Solving 9p + -18p2 + 8p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(9 + -18p + 8p2) = 0 Factor a trinomial. p((3 + -4p)(3 + -2p)) = 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 + -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 = 0.75Subproblem 3
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 = 1.5Solution
p = {0, 0.75, 1.5}
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