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Simplifying (2p + -3)(-3p + 4) = 0 Reorder the terms: (-3 + 2p)(-3p + 4) = 0 Reorder the terms: (-3 + 2p)(4 + -3p) = 0 Multiply (-3 + 2p) * (4 + -3p) (-3(4 + -3p) + 2p * (4 + -3p)) = 0 ((4 * -3 + -3p * -3) + 2p * (4 + -3p)) = 0 ((-12 + 9p) + 2p * (4 + -3p)) = 0 (-12 + 9p + (4 * 2p + -3p * 2p)) = 0 (-12 + 9p + (8p + -6p2)) = 0 Combine like terms: 9p + 8p = 17p (-12 + 17p + -6p2) = 0 Solving -12 + 17p + -6p2 = 0 Solving for variable 'p'. Factor a trinomial. (-3 + 2p)(4 + -3p) = 0Subproblem 1
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 = 1.5Subproblem 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 = {1.5, 1.333333333}
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