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Simplifying (3p + -8)(p + 9) = 0 Reorder the terms: (-8 + 3p)(p + 9) = 0 Reorder the terms: (-8 + 3p)(9 + p) = 0 Multiply (-8 + 3p) * (9 + p) (-8(9 + p) + 3p * (9 + p)) = 0 ((9 * -8 + p * -8) + 3p * (9 + p)) = 0 ((-72 + -8p) + 3p * (9 + p)) = 0 (-72 + -8p + (9 * 3p + p * 3p)) = 0 (-72 + -8p + (27p + 3p2)) = 0 Combine like terms: -8p + 27p = 19p (-72 + 19p + 3p2) = 0 Solving -72 + 19p + 3p2 = 0 Solving for variable 'p'. Factor a trinomial. (-9 + -1p)(8 + -3p) = 0Subproblem 1
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 = -9Subproblem 2
Set the factor '(8 + -3p)' equal to zero and attempt to solve: Simplifying 8 + -3p = 0 Solving 8 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3p = 0 + -8 -3p = 0 + -8 Combine like terms: 0 + -8 = -8 -3p = -8 Divide each side by '-3'. p = 2.666666667 Simplifying p = 2.666666667Solution
p = {-9, 2.666666667}
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