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Simplifying (5p + -2)(4p + -5) = 0 Reorder the terms: (-2 + 5p)(4p + -5) = 0 Reorder the terms: (-2 + 5p)(-5 + 4p) = 0 Multiply (-2 + 5p) * (-5 + 4p) (-2(-5 + 4p) + 5p * (-5 + 4p)) = 0 ((-5 * -2 + 4p * -2) + 5p * (-5 + 4p)) = 0 ((10 + -8p) + 5p * (-5 + 4p)) = 0 (10 + -8p + (-5 * 5p + 4p * 5p)) = 0 (10 + -8p + (-25p + 20p2)) = 0 Combine like terms: -8p + -25p = -33p (10 + -33p + 20p2) = 0 Solving 10 + -33p + 20p2 = 0 Solving for variable 'p'. Factor a trinomial. (2 + -5p)(5 + -4p) = 0Subproblem 1
Set the factor '(2 + -5p)' equal to zero and attempt to solve: Simplifying 2 + -5p = 0 Solving 2 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5p = 0 + -2 -5p = 0 + -2 Combine like terms: 0 + -2 = -2 -5p = -2 Divide each side by '-5'. p = 0.4 Simplifying p = 0.4Subproblem 2
Set the factor '(5 + -4p)' equal to zero and attempt to solve: Simplifying 5 + -4p = 0 Solving 5 + -4p = 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 + -4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4p = 0 + -5 -4p = 0 + -5 Combine like terms: 0 + -5 = -5 -4p = -5 Divide each side by '-4'. p = 1.25 Simplifying p = 1.25Solution
p = {0.4, 1.25}
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