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Simplifying (5p + 3)(8p + 7) = 0 Reorder the terms: (3 + 5p)(8p + 7) = 0 Reorder the terms: (3 + 5p)(7 + 8p) = 0 Multiply (3 + 5p) * (7 + 8p) (3(7 + 8p) + 5p * (7 + 8p)) = 0 ((7 * 3 + 8p * 3) + 5p * (7 + 8p)) = 0 ((21 + 24p) + 5p * (7 + 8p)) = 0 (21 + 24p + (7 * 5p + 8p * 5p)) = 0 (21 + 24p + (35p + 40p2)) = 0 Combine like terms: 24p + 35p = 59p (21 + 59p + 40p2) = 0 Solving 21 + 59p + 40p2 = 0 Solving for variable 'p'. Factor a trinomial. (7 + 8p)(3 + 5p) = 0Subproblem 1
Set the factor '(7 + 8p)' equal to zero and attempt to solve: Simplifying 7 + 8p = 0 Solving 7 + 8p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 8p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8p = 0 + -7 8p = 0 + -7 Combine like terms: 0 + -7 = -7 8p = -7 Divide each side by '8'. p = -0.875 Simplifying p = -0.875Subproblem 2
Set the factor '(3 + 5p)' equal to zero and attempt to solve: Simplifying 3 + 5p = 0 Solving 3 + 5p = 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 + 5p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5p = 0 + -3 5p = 0 + -3 Combine like terms: 0 + -3 = -3 5p = -3 Divide each side by '5'. p = -0.6 Simplifying p = -0.6Solution
p = {-0.875, -0.6}
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