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Simplifying 3p + 3 = p2 + -5p + 18 Reorder the terms: 3 + 3p = p2 + -5p + 18 Reorder the terms: 3 + 3p = 18 + -5p + p2 Solving 3 + 3p = 18 + -5p + p2 Solving for variable 'p'. Reorder the terms: 3 + -18 + 3p + 5p + -1p2 = 18 + -5p + p2 + -18 + 5p + -1p2 Combine like terms: 3 + -18 = -15 -15 + 3p + 5p + -1p2 = 18 + -5p + p2 + -18 + 5p + -1p2 Combine like terms: 3p + 5p = 8p -15 + 8p + -1p2 = 18 + -5p + p2 + -18 + 5p + -1p2 Reorder the terms: -15 + 8p + -1p2 = 18 + -18 + -5p + 5p + p2 + -1p2 Combine like terms: 18 + -18 = 0 -15 + 8p + -1p2 = 0 + -5p + 5p + p2 + -1p2 -15 + 8p + -1p2 = -5p + 5p + p2 + -1p2 Combine like terms: -5p + 5p = 0 -15 + 8p + -1p2 = 0 + p2 + -1p2 -15 + 8p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -15 + 8p + -1p2 = 0 Factor a trinomial. (-5 + p)(3 + -1p) = 0Subproblem 1
Set the factor '(-5 + p)' equal to zero and attempt to solve: Simplifying -5 + p = 0 Solving -5 + p = 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 + p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + p = 0 + 5 p = 0 + 5 Combine like terms: 0 + 5 = 5 p = 5 Simplifying p = 5Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 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 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Solution
p = {5, 3}
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