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Simplifying 6p + 15 = p2 + 8p + 16 Reorder the terms: 15 + 6p = p2 + 8p + 16 Reorder the terms: 15 + 6p = 16 + 8p + p2 Solving 15 + 6p = 16 + 8p + p2 Solving for variable 'p'. Reorder the terms: 15 + -16 + 6p + -8p + -1p2 = 16 + 8p + p2 + -16 + -8p + -1p2 Combine like terms: 15 + -16 = -1 -1 + 6p + -8p + -1p2 = 16 + 8p + p2 + -16 + -8p + -1p2 Combine like terms: 6p + -8p = -2p -1 + -2p + -1p2 = 16 + 8p + p2 + -16 + -8p + -1p2 Reorder the terms: -1 + -2p + -1p2 = 16 + -16 + 8p + -8p + p2 + -1p2 Combine like terms: 16 + -16 = 0 -1 + -2p + -1p2 = 0 + 8p + -8p + p2 + -1p2 -1 + -2p + -1p2 = 8p + -8p + p2 + -1p2 Combine like terms: 8p + -8p = 0 -1 + -2p + -1p2 = 0 + p2 + -1p2 -1 + -2p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -1 + -2p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2p + p2) = 0 Factor a trinomial. -1((1 + p)(1 + p)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 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 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 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 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Solution
p = {-1, -1}
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