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Simplifying (-5p + 8)(7p + -5) = 0 Reorder the terms: (8 + -5p)(7p + -5) = 0 Reorder the terms: (8 + -5p)(-5 + 7p) = 0 Multiply (8 + -5p) * (-5 + 7p) (8(-5 + 7p) + -5p * (-5 + 7p)) = 0 ((-5 * 8 + 7p * 8) + -5p * (-5 + 7p)) = 0 ((-40 + 56p) + -5p * (-5 + 7p)) = 0 (-40 + 56p + (-5 * -5p + 7p * -5p)) = 0 (-40 + 56p + (25p + -35p2)) = 0 Combine like terms: 56p + 25p = 81p (-40 + 81p + -35p2) = 0 Solving -40 + 81p + -35p2 = 0 Solving for variable 'p'. Factor a trinomial. (-8 + 5p)(5 + -7p) = 0Subproblem 1
Set the factor '(-8 + 5p)' equal to zero and attempt to solve: Simplifying -8 + 5p = 0 Solving -8 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5p = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5p = 0 + 8 5p = 0 + 8 Combine like terms: 0 + 8 = 8 5p = 8 Divide each side by '5'. p = 1.6 Simplifying p = 1.6Subproblem 2
Set the factor '(5 + -7p)' equal to zero and attempt to solve: Simplifying 5 + -7p = 0 Solving 5 + -7p = 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 + -7p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7p = 0 + -5 -7p = 0 + -5 Combine like terms: 0 + -5 = -5 -7p = -5 Divide each side by '-7'. p = 0.7142857143 Simplifying p = 0.7142857143Solution
p = {1.6, 0.7142857143}
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