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Simplifying (8p + -6)(3p + -5) = 0 Reorder the terms: (-6 + 8p)(3p + -5) = 0 Reorder the terms: (-6 + 8p)(-5 + 3p) = 0 Multiply (-6 + 8p) * (-5 + 3p) (-6(-5 + 3p) + 8p * (-5 + 3p)) = 0 ((-5 * -6 + 3p * -6) + 8p * (-5 + 3p)) = 0 ((30 + -18p) + 8p * (-5 + 3p)) = 0 (30 + -18p + (-5 * 8p + 3p * 8p)) = 0 (30 + -18p + (-40p + 24p2)) = 0 Combine like terms: -18p + -40p = -58p (30 + -58p + 24p2) = 0 Solving 30 + -58p + 24p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -29p + 12p2) = 0 Factor a trinomial. 2((3 + -4p)(5 + -3p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Subproblem 2
Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 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 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Solution
p = {0.75, 1.666666667}
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