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Simplifying (p + 4)(3p + 6) = 0 Reorder the terms: (4 + p)(3p + 6) = 0 Reorder the terms: (4 + p)(6 + 3p) = 0 Multiply (4 + p) * (6 + 3p) (4(6 + 3p) + p(6 + 3p)) = 0 ((6 * 4 + 3p * 4) + p(6 + 3p)) = 0 ((24 + 12p) + p(6 + 3p)) = 0 (24 + 12p + (6 * p + 3p * p)) = 0 (24 + 12p + (6p + 3p2)) = 0 Combine like terms: 12p + 6p = 18p (24 + 18p + 3p2) = 0 Solving 24 + 18p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 6p + p2) = 0 Factor a trinomial. 3((4 + p)(2 + p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Subproblem 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 = {-4, -2}
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