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Simplifying (3p + -4)(2p + 5) = 0 Reorder the terms: (-4 + 3p)(2p + 5) = 0 Reorder the terms: (-4 + 3p)(5 + 2p) = 0 Multiply (-4 + 3p) * (5 + 2p) (-4(5 + 2p) + 3p * (5 + 2p)) = 0 ((5 * -4 + 2p * -4) + 3p * (5 + 2p)) = 0 ((-20 + -8p) + 3p * (5 + 2p)) = 0 (-20 + -8p + (5 * 3p + 2p * 3p)) = 0 (-20 + -8p + (15p + 6p2)) = 0 Combine like terms: -8p + 15p = 7p (-20 + 7p + 6p2) = 0 Solving -20 + 7p + 6p2 = 0 Solving for variable 'p'. Factor a trinomial. (-5 + -2p)(4 + -3p) = 0Subproblem 1
Set the factor '(-5 + -2p)' equal to zero and attempt to solve: Simplifying -5 + -2p = 0 Solving -5 + -2p = 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 + -2p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2p = 0 + 5 -2p = 0 + 5 Combine like terms: 0 + 5 = 5 -2p = 5 Divide each side by '-2'. p = -2.5 Simplifying p = -2.5Subproblem 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 = {-2.5, 1.333333333}
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