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Simplifying -4p2 + 5p + -18 = -5p2 + p + 27 Reorder the terms: -18 + 5p + -4p2 = -5p2 + p + 27 Reorder the terms: -18 + 5p + -4p2 = 27 + p + -5p2 Solving -18 + 5p + -4p2 = 27 + p + -5p2 Solving for variable 'p'. Reorder the terms: -18 + -27 + 5p + -1p + -4p2 + 5p2 = 27 + p + -5p2 + -27 + -1p + 5p2 Combine like terms: -18 + -27 = -45 -45 + 5p + -1p + -4p2 + 5p2 = 27 + p + -5p2 + -27 + -1p + 5p2 Combine like terms: 5p + -1p = 4p -45 + 4p + -4p2 + 5p2 = 27 + p + -5p2 + -27 + -1p + 5p2 Combine like terms: -4p2 + 5p2 = 1p2 -45 + 4p + 1p2 = 27 + p + -5p2 + -27 + -1p + 5p2 Reorder the terms: -45 + 4p + 1p2 = 27 + -27 + p + -1p + -5p2 + 5p2 Combine like terms: 27 + -27 = 0 -45 + 4p + 1p2 = 0 + p + -1p + -5p2 + 5p2 -45 + 4p + 1p2 = p + -1p + -5p2 + 5p2 Combine like terms: p + -1p = 0 -45 + 4p + 1p2 = 0 + -5p2 + 5p2 -45 + 4p + 1p2 = -5p2 + 5p2 Combine like terms: -5p2 + 5p2 = 0 -45 + 4p + 1p2 = 0 Factor a trinomial. (-9 + -1p)(5 + -1p) = 0Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 2
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 = 5Solution
p = {-9, 5}
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