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Simplifying 3p3 = 2p2 + 5p Reorder the terms: 3p3 = 5p + 2p2 Solving 3p3 = 5p + 2p2 Solving for variable 'p'. Reorder the terms: -5p + -2p2 + 3p3 = 5p + 2p2 + -5p + -2p2 Reorder the terms: -5p + -2p2 + 3p3 = 5p + -5p + 2p2 + -2p2 Combine like terms: 5p + -5p = 0 -5p + -2p2 + 3p3 = 0 + 2p2 + -2p2 -5p + -2p2 + 3p3 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 -5p + -2p2 + 3p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-5 + -2p + 3p2) = 0 Factor a trinomial. p((-1 + -1p)(5 + -3p)) = 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 + -1p)' equal to zero and attempt to solve: Simplifying -1 + -1p = 0 Solving -1 + -1p = 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 + -1p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1p = 0 + 1 -1p = 0 + 1 Combine like terms: 0 + 1 = 1 -1p = 1 Divide each side by '-1'. p = -1 Simplifying p = -1Subproblem 3
Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 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 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Solution
p = {0, -1, 1.666666667}
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