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Simplifying (8p + -6)(2p + -2) = 0 Reorder the terms: (-6 + 8p)(2p + -2) = 0 Reorder the terms: (-6 + 8p)(-2 + 2p) = 0 Multiply (-6 + 8p) * (-2 + 2p) (-6(-2 + 2p) + 8p * (-2 + 2p)) = 0 ((-2 * -6 + 2p * -6) + 8p * (-2 + 2p)) = 0 ((12 + -12p) + 8p * (-2 + 2p)) = 0 (12 + -12p + (-2 * 8p + 2p * 8p)) = 0 (12 + -12p + (-16p + 16p2)) = 0 Combine like terms: -12p + -16p = -28p (12 + -28p + 16p2) = 0 Solving 12 + -28p + 16p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -7p + 4p2) = 0 Factor a trinomial. 4((3 + -4p)(1 + -1p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 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 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {0.75, 1}
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