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Simplifying (4p + -3)(2p + 8) = 0 Reorder the terms: (-3 + 4p)(2p + 8) = 0 Reorder the terms: (-3 + 4p)(8 + 2p) = 0 Multiply (-3 + 4p) * (8 + 2p) (-3(8 + 2p) + 4p * (8 + 2p)) = 0 ((8 * -3 + 2p * -3) + 4p * (8 + 2p)) = 0 ((-24 + -6p) + 4p * (8 + 2p)) = 0 (-24 + -6p + (8 * 4p + 2p * 4p)) = 0 (-24 + -6p + (32p + 8p2)) = 0 Combine like terms: -6p + 32p = 26p (-24 + 26p + 8p2) = 0 Solving -24 + 26p + 8p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 13p + 4p2) = 0 Factor a trinomial. 2((-4 + -1p)(3 + -4p)) = 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 '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Solution
p = {-4, 0.75}
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