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Simplifying 0 = 6r2 + -23r + 20 Reorder the terms: 0 = 20 + -23r + 6r2 Solving 0 = 20 + -23r + 6r2 Solving for variable 'r'. Combine like terms: 0 + -20 = -20 -20 + 23r + -6r2 = 20 + -23r + 6r2 + -20 + 23r + -6r2 Reorder the terms: -20 + 23r + -6r2 = 20 + -20 + -23r + 23r + 6r2 + -6r2 Combine like terms: 20 + -20 = 0 -20 + 23r + -6r2 = 0 + -23r + 23r + 6r2 + -6r2 -20 + 23r + -6r2 = -23r + 23r + 6r2 + -6r2 Combine like terms: -23r + 23r = 0 -20 + 23r + -6r2 = 0 + 6r2 + -6r2 -20 + 23r + -6r2 = 6r2 + -6r2 Combine like terms: 6r2 + -6r2 = 0 -20 + 23r + -6r2 = 0 Factor a trinomial. (-5 + 2r)(4 + -3r) = 0Subproblem 1
Set the factor '(-5 + 2r)' equal to zero and attempt to solve: Simplifying -5 + 2r = 0 Solving -5 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2r = 0 + 5 2r = 0 + 5 Combine like terms: 0 + 5 = 5 2r = 5 Divide each side by '2'. r = 2.5 Simplifying r = 2.5Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {2.5, 1.333333333}
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