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Simplifying 29p2 + 10p = -10p3 Reorder the terms: 10p + 29p2 = -10p3 Solving 10p + 29p2 = -10p3 Solving for variable 'p'. Combine like terms: -10p3 + 10p3 = 0 10p + 29p2 + 10p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(10 + 29p + 10p2) = 0 Factor a trinomial. p((5 + 2p)(2 + 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 '(5 + 2p)' equal to zero and attempt to solve: Simplifying 5 + 2p = 0 Solving 5 + 2p = 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 + 2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2p = 0 + -5 2p = 0 + -5 Combine like terms: 0 + -5 = -5 2p = -5 Divide each side by '2'. p = -2.5 Simplifying p = -2.5Subproblem 3
Set the factor '(2 + 5p)' equal to zero and attempt to solve: Simplifying 2 + 5p = 0 Solving 2 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5p = 0 + -2 5p = 0 + -2 Combine like terms: 0 + -2 = -2 5p = -2 Divide each side by '5'. p = -0.4 Simplifying p = -0.4Solution
p = {0, -2.5, -0.4}
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