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