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Simplifying 4p(3p + -5) + -3(3p + -5) = 0 Reorder the terms: 4p(-5 + 3p) + -3(3p + -5) = 0 (-5 * 4p + 3p * 4p) + -3(3p + -5) = 0 (-20p + 12p2) + -3(3p + -5) = 0 Reorder the terms: -20p + 12p2 + -3(-5 + 3p) = 0 -20p + 12p2 + (-5 * -3 + 3p * -3) = 0 -20p + 12p2 + (15 + -9p) = 0 Reorder the terms: 15 + -20p + -9p + 12p2 = 0 Combine like terms: -20p + -9p = -29p 15 + -29p + 12p2 = 0 Solving 15 + -29p + 12p2 = 0 Solving for variable 'p'. Factor a trinomial. (3 + -4p)(5 + -3p) = 0Subproblem 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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