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Simplifying (3p + -5)(8p + 6) = 0 Reorder the terms: (-5 + 3p)(8p + 6) = 0 Reorder the terms: (-5 + 3p)(6 + 8p) = 0 Multiply (-5 + 3p) * (6 + 8p) (-5(6 + 8p) + 3p * (6 + 8p)) = 0 ((6 * -5 + 8p * -5) + 3p * (6 + 8p)) = 0 ((-30 + -40p) + 3p * (6 + 8p)) = 0 (-30 + -40p + (6 * 3p + 8p * 3p)) = 0 (-30 + -40p + (18p + 24p2)) = 0 Combine like terms: -40p + 18p = -22p (-30 + -22p + 24p2) = 0 Solving -30 + -22p + 24p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -11p + 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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