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Simplifying 3p2 + -9p = 84 Reorder the terms: -9p + 3p2 = 84 Solving -9p + 3p2 = 84 Solving for variable 'p'. Reorder the terms: -84 + -9p + 3p2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -9p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + -3p + p2) = 0 Factor a trinomial. 3((-4 + -1p)(7 + -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 '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-4, 7}
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