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Simplifying 6p2 = 9p + 132 Reorder the terms: 6p2 = 132 + 9p Solving 6p2 = 132 + 9p Solving for variable 'p'. Reorder the terms: -132 + -9p + 6p2 = 132 + 9p + -132 + -9p Reorder the terms: -132 + -9p + 6p2 = 132 + -132 + 9p + -9p Combine like terms: 132 + -132 = 0 -132 + -9p + 6p2 = 0 + 9p + -9p -132 + -9p + 6p2 = 9p + -9p Combine like terms: 9p + -9p = 0 -132 + -9p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-44 + -3p + 2p2) = 0 Factor a trinomial. 3((-4 + -1p)(11 + -2p)) = 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 '(11 + -2p)' equal to zero and attempt to solve: Simplifying 11 + -2p = 0 Solving 11 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2p = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2p = 0 + -11 -2p = 0 + -11 Combine like terms: 0 + -11 = -11 -2p = -11 Divide each side by '-2'. p = 5.5 Simplifying p = 5.5Solution
p = {-4, 5.5}
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