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Simplifying 5p3 + 39p2 = 8p Reorder the terms: 39p2 + 5p3 = 8p Solving 39p2 + 5p3 = 8p Solving for variable 'p'. Reorder the terms: -8p + 39p2 + 5p3 = 8p + -8p Combine like terms: 8p + -8p = 0 -8p + 39p2 + 5p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-8 + 39p + 5p2) = 0 Factor a trinomial. p((-8 + -1p)(1 + -5p)) = 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 '(-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 = -8Subproblem 3
Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 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 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2Solution
p = {0, -8, 0.2}
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