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Simplifying (2p + 4)(4p + -4) = 0 Reorder the terms: (4 + 2p)(4p + -4) = 0 Reorder the terms: (4 + 2p)(-4 + 4p) = 0 Multiply (4 + 2p) * (-4 + 4p) (4(-4 + 4p) + 2p * (-4 + 4p)) = 0 ((-4 * 4 + 4p * 4) + 2p * (-4 + 4p)) = 0 ((-16 + 16p) + 2p * (-4 + 4p)) = 0 (-16 + 16p + (-4 * 2p + 4p * 2p)) = 0 (-16 + 16p + (-8p + 8p2)) = 0 Combine like terms: 16p + -8p = 8p (-16 + 8p + 8p2) = 0 Solving -16 + 8p + 8p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + p + p2) = 0 Factor a trinomial. 8((-2 + -1p)(1 + -1p)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 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 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {-2, 1}
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