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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 = 2p (-35 + 2p + p2) = 0 Solving -35 + 2p + p2 = 0 Solving for variable 'p'. Factor a trinomial. (-7 + -1p)(5 + -1p) = 0Subproblem 1
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 = -7Subproblem 2
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 = 5Solution
p = {-7, 5}
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