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Simplifying 6p2 = -27p + -12 Reorder the terms: 6p2 = -12 + -27p Solving 6p2 = -12 + -27p Solving for variable 'p'. Reorder the terms: 12 + 27p + 6p2 = -12 + -27p + 12 + 27p Reorder the terms: 12 + 27p + 6p2 = -12 + 12 + -27p + 27p Combine like terms: -12 + 12 = 0 12 + 27p + 6p2 = 0 + -27p + 27p 12 + 27p + 6p2 = -27p + 27p Combine like terms: -27p + 27p = 0 12 + 27p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 9p + 2p2) = 0 Factor a trinomial. 3((4 + p)(1 + 2p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Subproblem 2
Set the factor '(1 + 2p)' equal to zero and attempt to solve: Simplifying 1 + 2p = 0 Solving 1 + 2p = 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 + 2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2p = 0 + -1 2p = 0 + -1 Combine like terms: 0 + -1 = -1 2p = -1 Divide each side by '2'. p = -0.5 Simplifying p = -0.5Solution
p = {-4, -0.5}
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