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Simplifying (2p + -1)(p + 3) + -1(7p + 4)(p + 3) = 0 Reorder the terms: (-1 + 2p)(p + 3) + -1(7p + 4)(p + 3) = 0 Reorder the terms: (-1 + 2p)(3 + p) + -1(7p + 4)(p + 3) = 0 Multiply (-1 + 2p) * (3 + p) (-1(3 + p) + 2p * (3 + p)) + -1(7p + 4)(p + 3) = 0 ((3 * -1 + p * -1) + 2p * (3 + p)) + -1(7p + 4)(p + 3) = 0 ((-3 + -1p) + 2p * (3 + p)) + -1(7p + 4)(p + 3) = 0 (-3 + -1p + (3 * 2p + p * 2p)) + -1(7p + 4)(p + 3) = 0 (-3 + -1p + (6p + 2p2)) + -1(7p + 4)(p + 3) = 0 Combine like terms: -1p + 6p = 5p (-3 + 5p + 2p2) + -1(7p + 4)(p + 3) = 0 Reorder the terms: -3 + 5p + 2p2 + -1(4 + 7p)(p + 3) = 0 Reorder the terms: -3 + 5p + 2p2 + -1(4 + 7p)(3 + p) = 0 Multiply (4 + 7p) * (3 + p) -3 + 5p + 2p2 + -1(4(3 + p) + 7p * (3 + p)) = 0 -3 + 5p + 2p2 + -1((3 * 4 + p * 4) + 7p * (3 + p)) = 0 -3 + 5p + 2p2 + -1((12 + 4p) + 7p * (3 + p)) = 0 -3 + 5p + 2p2 + -1(12 + 4p + (3 * 7p + p * 7p)) = 0 -3 + 5p + 2p2 + -1(12 + 4p + (21p + 7p2)) = 0 Combine like terms: 4p + 21p = 25p -3 + 5p + 2p2 + -1(12 + 25p + 7p2) = 0 -3 + 5p + 2p2 + (12 * -1 + 25p * -1 + 7p2 * -1) = 0 -3 + 5p + 2p2 + (-12 + -25p + -7p2) = 0 Reorder the terms: -3 + -12 + 5p + -25p + 2p2 + -7p2 = 0 Combine like terms: -3 + -12 = -15 -15 + 5p + -25p + 2p2 + -7p2 = 0 Combine like terms: 5p + -25p = -20p -15 + -20p + 2p2 + -7p2 = 0 Combine like terms: 2p2 + -7p2 = -5p2 -15 + -20p + -5p2 = 0 Solving -15 + -20p + -5p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-5'. -5(3 + 4p + p2) = 0 Factor a trinomial. -5((3 + p)(1 + p)) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 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 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Solution
p = {-3, -1}
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