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Simplifying -2p2 = 16p + 24 Reorder the terms: -2p2 = 24 + 16p Solving -2p2 = 24 + 16p Solving for variable 'p'. Reorder the terms: -24 + -16p + -2p2 = 24 + 16p + -24 + -16p Reorder the terms: -24 + -16p + -2p2 = 24 + -24 + 16p + -16p Combine like terms: 24 + -24 = 0 -24 + -16p + -2p2 = 0 + 16p + -16p -24 + -16p + -2p2 = 16p + -16p Combine like terms: 16p + -16p = 0 -24 + -16p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(12 + 8p + p2) = 0 Factor a trinomial. -2((6 + p)(2 + p)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6 + p)' equal to zero and attempt to solve: Simplifying 6 + p = 0 Solving 6 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + p = 0 + -6 p = 0 + -6 Combine like terms: 0 + -6 = -6 p = -6 Simplifying p = -6Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Solution
p = {-6, -2}
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