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Simplifying -3r2 + 24r + -45 = 0 Reorder the terms: -45 + 24r + -3r2 = 0 Solving -45 + 24r + -3r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 8r + -1r2) = 0 Factor a trinomial. 3((-5 + r)(3 + -1r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + r)' equal to zero and attempt to solve: Simplifying -5 + r = 0 Solving -5 + r = 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 + r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + r = 0 + 5 r = 0 + 5 Combine like terms: 0 + 5 = 5 r = 5 Simplifying r = 5Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {5, 3}
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