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Simplifying (p + -2)(p + -7) + (2p + -1)(p + 8) = p(2p + 3) + 24 Reorder the terms: (-2 + p)(p + -7) + (2p + -1)(p + 8) = p(2p + 3) + 24 Reorder the terms: (-2 + p)(-7 + p) + (2p + -1)(p + 8) = p(2p + 3) + 24 Multiply (-2 + p) * (-7 + p) (-2(-7 + p) + p(-7 + p)) + (2p + -1)(p + 8) = p(2p + 3) + 24 ((-7 * -2 + p * -2) + p(-7 + p)) + (2p + -1)(p + 8) = p(2p + 3) + 24 ((14 + -2p) + p(-7 + p)) + (2p + -1)(p + 8) = p(2p + 3) + 24 (14 + -2p + (-7 * p + p * p)) + (2p + -1)(p + 8) = p(2p + 3) + 24 (14 + -2p + (-7p + p2)) + (2p + -1)(p + 8) = p(2p + 3) + 24 Combine like terms: -2p + -7p = -9p (14 + -9p + p2) + (2p + -1)(p + 8) = p(2p + 3) + 24 Reorder the terms: 14 + -9p + p2 + (-1 + 2p)(p + 8) = p(2p + 3) + 24 Reorder the terms: 14 + -9p + p2 + (-1 + 2p)(8 + p) = p(2p + 3) + 24 Multiply (-1 + 2p) * (8 + p) 14 + -9p + p2 + (-1(8 + p) + 2p * (8 + p)) = p(2p + 3) + 24 14 + -9p + p2 + ((8 * -1 + p * -1) + 2p * (8 + p)) = p(2p + 3) + 24 14 + -9p + p2 + ((-8 + -1p) + 2p * (8 + p)) = p(2p + 3) + 24 14 + -9p + p2 + (-8 + -1p + (8 * 2p + p * 2p)) = p(2p + 3) + 24 14 + -9p + p2 + (-8 + -1p + (16p + 2p2)) = p(2p + 3) + 24 Combine like terms: -1p + 16p = 15p 14 + -9p + p2 + (-8 + 15p + 2p2) = p(2p + 3) + 24 Reorder the terms: 14 + -8 + -9p + 15p + p2 + 2p2 = p(2p + 3) + 24 Combine like terms: 14 + -8 = 6 6 + -9p + 15p + p2 + 2p2 = p(2p + 3) + 24 Combine like terms: -9p + 15p = 6p 6 + 6p + p2 + 2p2 = p(2p + 3) + 24 Combine like terms: p2 + 2p2 = 3p2 6 + 6p + 3p2 = p(2p + 3) + 24 Reorder the terms: 6 + 6p + 3p2 = p(3 + 2p) + 24 6 + 6p + 3p2 = (3 * p + 2p * p) + 24 6 + 6p + 3p2 = (3p + 2p2) + 24 Reorder the terms: 6 + 6p + 3p2 = 24 + 3p + 2p2 Solving 6 + 6p + 3p2 = 24 + 3p + 2p2 Solving for variable 'p'. Reorder the terms: 6 + -24 + 6p + -3p + 3p2 + -2p2 = 24 + 3p + 2p2 + -24 + -3p + -2p2 Combine like terms: 6 + -24 = -18 -18 + 6p + -3p + 3p2 + -2p2 = 24 + 3p + 2p2 + -24 + -3p + -2p2 Combine like terms: 6p + -3p = 3p -18 + 3p + 3p2 + -2p2 = 24 + 3p + 2p2 + -24 + -3p + -2p2 Combine like terms: 3p2 + -2p2 = 1p2 -18 + 3p + 1p2 = 24 + 3p + 2p2 + -24 + -3p + -2p2 Reorder the terms: -18 + 3p + 1p2 = 24 + -24 + 3p + -3p + 2p2 + -2p2 Combine like terms: 24 + -24 = 0 -18 + 3p + 1p2 = 0 + 3p + -3p + 2p2 + -2p2 -18 + 3p + 1p2 = 3p + -3p + 2p2 + -2p2 Combine like terms: 3p + -3p = 0 -18 + 3p + 1p2 = 0 + 2p2 + -2p2 -18 + 3p + 1p2 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 -18 + 3p + 1p2 = 0 Factor a trinomial. (-6 + -1p)(3 + -1p) = 0Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve: Simplifying -6 + -1p = 0 Solving -6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1p = 0 + 6 -1p = 0 + 6 Combine like terms: 0 + 6 = 6 -1p = 6 Divide each side by '-1'. p = -6 Simplifying p = -6Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 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 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Solution
p = {-6, 3}
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