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Simplifying (10p + 3)(-4p + 9) = 0 Reorder the terms: (3 + 10p)(-4p + 9) = 0 Reorder the terms: (3 + 10p)(9 + -4p) = 0 Multiply (3 + 10p) * (9 + -4p) (3(9 + -4p) + 10p * (9 + -4p)) = 0 ((9 * 3 + -4p * 3) + 10p * (9 + -4p)) = 0 ((27 + -12p) + 10p * (9 + -4p)) = 0 (27 + -12p + (9 * 10p + -4p * 10p)) = 0 (27 + -12p + (90p + -40p2)) = 0 Combine like terms: -12p + 90p = 78p (27 + 78p + -40p2) = 0 Solving 27 + 78p + -40p2 = 0 Solving for variable 'p'. Factor a trinomial. (9 + -4p)(3 + 10p) = 0Subproblem 1
Set the factor '(9 + -4p)' equal to zero and attempt to solve: Simplifying 9 + -4p = 0 Solving 9 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4p = 0 + -9 -4p = 0 + -9 Combine like terms: 0 + -9 = -9 -4p = -9 Divide each side by '-4'. p = 2.25 Simplifying p = 2.25Subproblem 2
Set the factor '(3 + 10p)' equal to zero and attempt to solve: Simplifying 3 + 10p = 0 Solving 3 + 10p = 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 + 10p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10p = 0 + -3 10p = 0 + -3 Combine like terms: 0 + -3 = -3 10p = -3 Divide each side by '10'. p = -0.3 Simplifying p = -0.3Solution
p = {2.25, -0.3}
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