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Simplifying (3p + 2)(p + -1) = 12 Reorder the terms: (2 + 3p)(p + -1) = 12 Reorder the terms: (2 + 3p)(-1 + p) = 12 Multiply (2 + 3p) * (-1 + p) (2(-1 + p) + 3p * (-1 + p)) = 12 ((-1 * 2 + p * 2) + 3p * (-1 + p)) = 12 ((-2 + 2p) + 3p * (-1 + p)) = 12 (-2 + 2p + (-1 * 3p + p * 3p)) = 12 (-2 + 2p + (-3p + 3p2)) = 12 Combine like terms: 2p + -3p = -1p (-2 + -1p + 3p2) = 12 Solving -2 + -1p + 3p2 = 12 Solving for variable 'p'. Reorder the terms: -2 + -12 + -1p + 3p2 = 12 + -12 Combine like terms: -2 + -12 = -14 -14 + -1p + 3p2 = 12 + -12 Combine like terms: 12 + -12 = 0 -14 + -1p + 3p2 = 0 Factor a trinomial. (-2 + -1p)(7 + -3p) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve: Simplifying 7 + -3p = 0 Solving 7 + -3p = 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 + -3p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3p = 0 + -7 -3p = 0 + -7 Combine like terms: 0 + -7 = -7 -3p = -7 Divide each side by '-3'. p = 2.333333333 Simplifying p = 2.333333333Solution
p = {-2, 2.333333333}
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