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Simplifying (p + 3)(p + -5) = p + 13 Reorder the terms: (3 + p)(p + -5) = p + 13 Reorder the terms: (3 + p)(-5 + p) = p + 13 Multiply (3 + p) * (-5 + p) (3(-5 + p) + p(-5 + p)) = p + 13 ((-5 * 3 + p * 3) + p(-5 + p)) = p + 13 ((-15 + 3p) + p(-5 + p)) = p + 13 (-15 + 3p + (-5 * p + p * p)) = p + 13 (-15 + 3p + (-5p + p2)) = p + 13 Combine like terms: 3p + -5p = -2p (-15 + -2p + p2) = p + 13 Reorder the terms: -15 + -2p + p2 = 13 + p Solving -15 + -2p + p2 = 13 + p Solving for variable 'p'. Reorder the terms: -15 + -13 + -2p + -1p + p2 = 13 + p + -13 + -1p Combine like terms: -15 + -13 = -28 -28 + -2p + -1p + p2 = 13 + p + -13 + -1p Combine like terms: -2p + -1p = -3p -28 + -3p + p2 = 13 + p + -13 + -1p Reorder the terms: -28 + -3p + p2 = 13 + -13 + p + -1p Combine like terms: 13 + -13 = 0 -28 + -3p + p2 = 0 + p + -1p -28 + -3p + p2 = p + -1p Combine like terms: p + -1p = 0 -28 + -3p + p2 = 0 Factor a trinomial. (-4 + -1p)(7 + -1p) = 0Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve: Simplifying -4 + -1p = 0 Solving -4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1p = 0 + 4 -1p = 0 + 4 Combine like terms: 0 + 4 = 4 -1p = 4 Divide each side by '-1'. p = -4 Simplifying p = -4Subproblem 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 = {-4, 7}
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