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Simplifying 2p2 = 12p + 54 Reorder the terms: 2p2 = 54 + 12p Solving 2p2 = 54 + 12p Solving for variable 'p'. Reorder the terms: -54 + -12p + 2p2 = 54 + 12p + -54 + -12p Reorder the terms: -54 + -12p + 2p2 = 54 + -54 + 12p + -12p Combine like terms: 54 + -54 = 0 -54 + -12p + 2p2 = 0 + 12p + -12p -54 + -12p + 2p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -54 + -12p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -6p + p2) = 0 Factor a trinomial. 2((-3 + -1p)(9 + -1p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve: Simplifying -3 + -1p = 0 Solving -3 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1p = 0 + 3 -1p = 0 + 3 Combine like terms: 0 + 3 = 3 -1p = 3 Divide each side by '-1'. p = -3 Simplifying p = -3Subproblem 2
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 = 9Solution
p = {-3, 9}
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