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Simplifying (7p + -5)(5p + -2) = 0 Reorder the terms: (-5 + 7p)(5p + -2) = 0 Reorder the terms: (-5 + 7p)(-2 + 5p) = 0 Multiply (-5 + 7p) * (-2 + 5p) (-5(-2 + 5p) + 7p * (-2 + 5p)) = 0 ((-2 * -5 + 5p * -5) + 7p * (-2 + 5p)) = 0 ((10 + -25p) + 7p * (-2 + 5p)) = 0 (10 + -25p + (-2 * 7p + 5p * 7p)) = 0 (10 + -25p + (-14p + 35p2)) = 0 Combine like terms: -25p + -14p = -39p (10 + -39p + 35p2) = 0 Solving 10 + -39p + 35p2 = 0 Solving for variable 'p'. Factor a trinomial. (2 + -5p)(5 + -7p) = 0Subproblem 1
Set the factor '(2 + -5p)' equal to zero and attempt to solve: Simplifying 2 + -5p = 0 Solving 2 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5p = 0 + -2 -5p = 0 + -2 Combine like terms: 0 + -2 = -2 -5p = -2 Divide each side by '-5'. p = 0.4 Simplifying p = 0.4Subproblem 2
Set the factor '(5 + -7p)' equal to zero and attempt to solve: Simplifying 5 + -7p = 0 Solving 5 + -7p = 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 + -7p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7p = 0 + -5 -7p = 0 + -5 Combine like terms: 0 + -5 = -5 -7p = -5 Divide each side by '-7'. p = 0.7142857143 Simplifying p = 0.7142857143Solution
p = {0.4, 0.7142857143}
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