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Simplifying 15p2 = 20 + 20p Solving 15p2 = 20 + 20p Solving for variable 'p'. Reorder the terms: -20 + -20p + 15p2 = 20 + 20p + -20 + -20p Reorder the terms: -20 + -20p + 15p2 = 20 + -20 + 20p + -20p Combine like terms: 20 + -20 = 0 -20 + -20p + 15p2 = 0 + 20p + -20p -20 + -20p + 15p2 = 20p + -20p Combine like terms: 20p + -20p = 0 -20 + -20p + 15p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -4p + 3p2) = 0 Factor a trinomial. 5((-2 + -3p)(2 + -1p)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -3p)' equal to zero and attempt to solve: Simplifying -2 + -3p = 0 Solving -2 + -3p = 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 + -3p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3p = 0 + 2 -3p = 0 + 2 Combine like terms: 0 + 2 = 2 -3p = 2 Divide each side by '-3'. p = -0.6666666667 Simplifying p = -0.6666666667Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 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 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-0.6666666667, 2}
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