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Simplifying 30p3 + 52p2 + 14p = 0 Reorder the terms: 14p + 52p2 + 30p3 = 0 Solving 14p + 52p2 + 30p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2p'. 2p(7 + 26p + 15p2) = 0 Factor a trinomial. 2p((7 + 5p)(1 + 3p)) = 0 Ignore the factor 2.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 '(7 + 5p)' equal to zero and attempt to solve: Simplifying 7 + 5p = 0 Solving 7 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5p = 0 + -7 5p = 0 + -7 Combine like terms: 0 + -7 = -7 5p = -7 Divide each side by '5'. p = -1.4 Simplifying p = -1.4Subproblem 3
Set the factor '(1 + 3p)' equal to zero and attempt to solve: Simplifying 1 + 3p = 0 Solving 1 + 3p = 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 + 3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3p = 0 + -1 3p = 0 + -1 Combine like terms: 0 + -1 = -1 3p = -1 Divide each side by '3'. p = -0.3333333333 Simplifying p = -0.3333333333Solution
p = {0, -1.4, -0.3333333333}
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