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Simplifying 3p2 + -6p + -81 = -9 Reorder the terms: -81 + -6p + 3p2 = -9 Solving -81 + -6p + 3p2 = -9 Solving for variable 'p'. Reorder the terms: -81 + 9 + -6p + 3p2 = -9 + 9 Combine like terms: -81 + 9 = -72 -72 + -6p + 3p2 = -9 + 9 Combine like terms: -9 + 9 = 0 -72 + -6p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + -2p + p2) = 0 Factor a trinomial. 3((-4 + -1p)(6 + -1p)) = 0 Ignore the factor 3.Subproblem 1
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 = -4Subproblem 2
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 = 6Solution
p = {-4, 6}
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