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Simplifying 2p2 + -12p + 28 = 4p + -4 Reorder the terms: 28 + -12p + 2p2 = 4p + -4 Reorder the terms: 28 + -12p + 2p2 = -4 + 4p Solving 28 + -12p + 2p2 = -4 + 4p Solving for variable 'p'. Reorder the terms: 28 + 4 + -12p + -4p + 2p2 = -4 + 4p + 4 + -4p Combine like terms: 28 + 4 = 32 32 + -12p + -4p + 2p2 = -4 + 4p + 4 + -4p Combine like terms: -12p + -4p = -16p 32 + -16p + 2p2 = -4 + 4p + 4 + -4p Reorder the terms: 32 + -16p + 2p2 = -4 + 4 + 4p + -4p Combine like terms: -4 + 4 = 0 32 + -16p + 2p2 = 0 + 4p + -4p 32 + -16p + 2p2 = 4p + -4p Combine like terms: 4p + -4p = 0 32 + -16p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -8p + p2) = 0 Factor a trinomial. 2((4 + -1p)(4 + -1p)) = 0 Ignore the factor 2.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 '(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 = 4Solution
p = {4, 4}
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