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Simplifying 3p2 + 24p + -27 = 0 Reorder the terms: -27 + 24p + 3p2 = 0 Solving -27 + 24p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 8p + p2) = 0 Factor a trinomial. 3((-9 + -1p)(1 + -1p)) = 0 Ignore the factor 3.Subproblem 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 '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {-9, 1}
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