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Simplifying (p + 9)(p + 2) = -12 Reorder the terms: (9 + p)(p + 2) = -12 Reorder the terms: (9 + p)(2 + p) = -12 Multiply (9 + p) * (2 + p) (9(2 + p) + p(2 + p)) = -12 ((2 * 9 + p * 9) + p(2 + p)) = -12 ((18 + 9p) + p(2 + p)) = -12 (18 + 9p + (2 * p + p * p)) = -12 (18 + 9p + (2p + p2)) = -12 Combine like terms: 9p + 2p = 11p (18 + 11p + p2) = -12 Solving 18 + 11p + p2 = -12 Solving for variable 'p'. Reorder the terms: 18 + 12 + 11p + p2 = -12 + 12 Combine like terms: 18 + 12 = 30 30 + 11p + p2 = -12 + 12 Combine like terms: -12 + 12 = 0 30 + 11p + p2 = 0 Factor a trinomial. (6 + p)(5 + p) = 0Subproblem 1
Set the factor '(6 + p)' equal to zero and attempt to solve: Simplifying 6 + p = 0 Solving 6 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + p = 0 + -6 p = 0 + -6 Combine like terms: 0 + -6 = -6 p = -6 Simplifying p = -6Subproblem 2
Set the factor '(5 + p)' equal to zero and attempt to solve: Simplifying 5 + p = 0 Solving 5 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + p = 0 + -5 p = 0 + -5 Combine like terms: 0 + -5 = -5 p = -5 Simplifying p = -5Solution
p = {-6, -5}
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