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Simplifying (4p + -2)(p + -4) = 0 Reorder the terms: (-2 + 4p)(p + -4) = 0 Reorder the terms: (-2 + 4p)(-4 + p) = 0 Multiply (-2 + 4p) * (-4 + p) (-2(-4 + p) + 4p * (-4 + p)) = 0 ((-4 * -2 + p * -2) + 4p * (-4 + p)) = 0 ((8 + -2p) + 4p * (-4 + p)) = 0 (8 + -2p + (-4 * 4p + p * 4p)) = 0 (8 + -2p + (-16p + 4p2)) = 0 Combine like terms: -2p + -16p = -18p (8 + -18p + 4p2) = 0 Solving 8 + -18p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -9p + 2p2) = 0 Factor a trinomial. 2((1 + -2p)(4 + -1p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2p)' equal to zero and attempt to solve: Simplifying 1 + -2p = 0 Solving 1 + -2p = 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 + -2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2p = 0 + -1 -2p = 0 + -1 Combine like terms: 0 + -1 = -1 -2p = -1 Divide each side by '-2'. p = 0.5 Simplifying p = 0.5Subproblem 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 = {0.5, 4}
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