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Simplifying (3p + 4)(9p + 3) = 0 Reorder the terms: (4 + 3p)(9p + 3) = 0 Reorder the terms: (4 + 3p)(3 + 9p) = 0 Multiply (4 + 3p) * (3 + 9p) (4(3 + 9p) + 3p * (3 + 9p)) = 0 ((3 * 4 + 9p * 4) + 3p * (3 + 9p)) = 0 ((12 + 36p) + 3p * (3 + 9p)) = 0 (12 + 36p + (3 * 3p + 9p * 3p)) = 0 (12 + 36p + (9p + 27p2)) = 0 Combine like terms: 36p + 9p = 45p (12 + 45p + 27p2) = 0 Solving 12 + 45p + 27p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 15p + 9p2) = 0 Factor a trinomial. 3((4 + 3p)(1 + 3p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 3p)' equal to zero and attempt to solve: Simplifying 4 + 3p = 0 Solving 4 + 3p = 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 + 3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3p = 0 + -4 3p = 0 + -4 Combine like terms: 0 + -4 = -4 3p = -4 Divide each side by '3'. p = -1.333333333 Simplifying p = -1.333333333Subproblem 2
Set the factor '(1 + 3p)' equal to zero and attempt to solve: Simplifying 1 + 3p = 0 Solving 1 + 3p = 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 + 3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3p = 0 + -1 3p = 0 + -1 Combine like terms: 0 + -1 = -1 3p = -1 Divide each side by '3'. p = -0.3333333333 Simplifying p = -0.3333333333Solution
p = {-1.333333333, -0.3333333333}
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