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Simplifying (p + -7)(p + -5) = 0 Reorder the terms: (-7 + p)(p + -5) = 0 Reorder the terms: (-7 + p)(-5 + p) = 0 Multiply (-7 + p) * (-5 + p) (-7(-5 + p) + p(-5 + p)) = 0 ((-5 * -7 + p * -7) + p(-5 + p)) = 0 ((35 + -7p) + p(-5 + p)) = 0 (35 + -7p + (-5 * p + p * p)) = 0 (35 + -7p + (-5p + p2)) = 0 Combine like terms: -7p + -5p = -12p (35 + -12p + p2) = 0 Solving 35 + -12p + p2 = 0 Solving for variable 'p'. Factor a trinomial. (5 + -1p)(7 + -1p) = 0Subproblem 1
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 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 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 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 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {5, 7}
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