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Simplifying 19p2 + 20p = 6p3 Reorder the terms: 20p + 19p2 = 6p3 Solving 20p + 19p2 = 6p3 Solving for variable 'p'. Combine like terms: 6p3 + -6p3 = 0 20p + 19p2 + -6p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(20 + 19p + -6p2) = 0 Factor a trinomial. p((4 + -1p)(5 + 6p)) = 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 '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Subproblem 3
Set the factor '(5 + 6p)' equal to zero and attempt to solve: Simplifying 5 + 6p = 0 Solving 5 + 6p = 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 + 6p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6p = 0 + -5 6p = 0 + -5 Combine like terms: 0 + -5 = -5 6p = -5 Divide each side by '6'. p = -0.8333333333 Simplifying p = -0.8333333333Solution
p = {0, 4, -0.8333333333}
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