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Simplifying (3p + -4)(5p + 9) = 0 Reorder the terms: (-4 + 3p)(5p + 9) = 0 Reorder the terms: (-4 + 3p)(9 + 5p) = 0 Multiply (-4 + 3p) * (9 + 5p) (-4(9 + 5p) + 3p * (9 + 5p)) = 0 ((9 * -4 + 5p * -4) + 3p * (9 + 5p)) = 0 ((-36 + -20p) + 3p * (9 + 5p)) = 0 (-36 + -20p + (9 * 3p + 5p * 3p)) = 0 (-36 + -20p + (27p + 15p2)) = 0 Combine like terms: -20p + 27p = 7p (-36 + 7p + 15p2) = 0 Solving -36 + 7p + 15p2 = 0 Solving for variable 'p'. Factor a trinomial. (-9 + -5p)(4 + -3p) = 0Subproblem 1
Set the factor '(-9 + -5p)' equal to zero and attempt to solve: Simplifying -9 + -5p = 0 Solving -9 + -5p = 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 + -5p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5p = 0 + 9 -5p = 0 + 9 Combine like terms: 0 + 9 = 9 -5p = 9 Divide each side by '-5'. p = -1.8 Simplifying p = -1.8Subproblem 2
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 = 1.333333333Solution
p = {-1.8, 1.333333333}
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