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Simplifying 4p(p + -1) + -24 = 3p(p + -2) Reorder the terms: 4p(-1 + p) + -24 = 3p(p + -2) (-1 * 4p + p * 4p) + -24 = 3p(p + -2) (-4p + 4p2) + -24 = 3p(p + -2) Reorder the terms: -24 + -4p + 4p2 = 3p(p + -2) Reorder the terms: -24 + -4p + 4p2 = 3p(-2 + p) -24 + -4p + 4p2 = (-2 * 3p + p * 3p) -24 + -4p + 4p2 = (-6p + 3p2) Solving -24 + -4p + 4p2 = -6p + 3p2 Solving for variable 'p'. Reorder the terms: -24 + -4p + 6p + 4p2 + -3p2 = -6p + 3p2 + 6p + -3p2 Combine like terms: -4p + 6p = 2p -24 + 2p + 4p2 + -3p2 = -6p + 3p2 + 6p + -3p2 Combine like terms: 4p2 + -3p2 = 1p2 -24 + 2p + 1p2 = -6p + 3p2 + 6p + -3p2 Reorder the terms: -24 + 2p + 1p2 = -6p + 6p + 3p2 + -3p2 Combine like terms: -6p + 6p = 0 -24 + 2p + 1p2 = 0 + 3p2 + -3p2 -24 + 2p + 1p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 -24 + 2p + 1p2 = 0 Factor a trinomial. (-6 + -1p)(4 + -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 '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-6, 4}
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