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Simplifying 2p(p + 5) + -3(p + 5) = 0 Reorder the terms: 2p(5 + p) + -3(p + 5) = 0 (5 * 2p + p * 2p) + -3(p + 5) = 0 (10p + 2p2) + -3(p + 5) = 0 Reorder the terms: 10p + 2p2 + -3(5 + p) = 0 10p + 2p2 + (5 * -3 + p * -3) = 0 10p + 2p2 + (-15 + -3p) = 0 Reorder the terms: -15 + 10p + -3p + 2p2 = 0 Combine like terms: 10p + -3p = 7p -15 + 7p + 2p2 = 0 Solving -15 + 7p + 2p2 = 0 Solving for variable 'p'. Factor a trinomial. (-5 + -1p)(3 + -2p) = 0Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 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 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve: Simplifying 3 + -2p = 0 Solving 3 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2p = 0 + -3 -2p = 0 + -3 Combine like terms: 0 + -3 = -3 -2p = -3 Divide each side by '-2'. p = 1.5 Simplifying p = 1.5Solution
p = {-5, 1.5}
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