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Simplifying (p + -2)(p + 4) + (p + -2)(p + 6) = 0 Reorder the terms: (-2 + p)(p + 4) + (p + -2)(p + 6) = 0 Reorder the terms: (-2 + p)(4 + p) + (p + -2)(p + 6) = 0 Multiply (-2 + p) * (4 + p) (-2(4 + p) + p(4 + p)) + (p + -2)(p + 6) = 0 ((4 * -2 + p * -2) + p(4 + p)) + (p + -2)(p + 6) = 0 ((-8 + -2p) + p(4 + p)) + (p + -2)(p + 6) = 0 (-8 + -2p + (4 * p + p * p)) + (p + -2)(p + 6) = 0 (-8 + -2p + (4p + p2)) + (p + -2)(p + 6) = 0 Combine like terms: -2p + 4p = 2p (-8 + 2p + p2) + (p + -2)(p + 6) = 0 Reorder the terms: -8 + 2p + p2 + (-2 + p)(p + 6) = 0 Reorder the terms: -8 + 2p + p2 + (-2 + p)(6 + p) = 0 Multiply (-2 + p) * (6 + p) -8 + 2p + p2 + (-2(6 + p) + p(6 + p)) = 0 -8 + 2p + p2 + ((6 * -2 + p * -2) + p(6 + p)) = 0 -8 + 2p + p2 + ((-12 + -2p) + p(6 + p)) = 0 -8 + 2p + p2 + (-12 + -2p + (6 * p + p * p)) = 0 -8 + 2p + p2 + (-12 + -2p + (6p + p2)) = 0 Combine like terms: -2p + 6p = 4p -8 + 2p + p2 + (-12 + 4p + p2) = 0 Reorder the terms: -8 + -12 + 2p + 4p + p2 + p2 = 0 Combine like terms: -8 + -12 = -20 -20 + 2p + 4p + p2 + p2 = 0 Combine like terms: 2p + 4p = 6p -20 + 6p + p2 + p2 = 0 Combine like terms: p2 + p2 = 2p2 -20 + 6p + 2p2 = 0 Solving -20 + 6p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 3p + p2) = 0 Factor a trinomial. 2((-5 + -1p)(2 + -1p)) = 0 Ignore the factor 2.Subproblem 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 '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 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 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-5, 2}
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