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Simplifying 27p3 + -162p2 + 240p = 0 Reorder the terms: 240p + -162p2 + 27p3 = 0 Solving 240p + -162p2 + 27p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3p'. 3p(80 + -54p + 9p2) = 0 Factor a trinomial. 3p((8 + -3p)(10 + -3p)) = 0 Ignore the factor 3.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 '(8 + -3p)' equal to zero and attempt to solve: Simplifying 8 + -3p = 0 Solving 8 + -3p = 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 + -3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3p = 0 + -8 -3p = 0 + -8 Combine like terms: 0 + -8 = -8 -3p = -8 Divide each side by '-3'. p = 2.666666667 Simplifying p = 2.666666667Subproblem 3
Set the factor '(10 + -3p)' equal to zero and attempt to solve: Simplifying 10 + -3p = 0 Solving 10 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3p = 0 + -10 -3p = 0 + -10 Combine like terms: 0 + -10 = -10 -3p = -10 Divide each side by '-3'. p = 3.333333333 Simplifying p = 3.333333333Solution
p = {0, 2.666666667, 3.333333333}
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