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Simplifying (11r + 5)(6r + -18) = 0 Reorder the terms: (5 + 11r)(6r + -18) = 0 Reorder the terms: (5 + 11r)(-18 + 6r) = 0 Multiply (5 + 11r) * (-18 + 6r) (5(-18 + 6r) + 11r * (-18 + 6r)) = 0 ((-18 * 5 + 6r * 5) + 11r * (-18 + 6r)) = 0 ((-90 + 30r) + 11r * (-18 + 6r)) = 0 (-90 + 30r + (-18 * 11r + 6r * 11r)) = 0 (-90 + 30r + (-198r + 66r2)) = 0 Combine like terms: 30r + -198r = -168r (-90 + -168r + 66r2) = 0 Solving -90 + -168r + 66r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + -28r + 11r2) = 0 Factor a trinomial. 6((-5 + -11r)(3 + -1r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + -11r)' equal to zero and attempt to solve: Simplifying -5 + -11r = 0 Solving -5 + -11r = 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 + -11r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -11r = 0 + 5 -11r = 0 + 5 Combine like terms: 0 + 5 = 5 -11r = 5 Divide each side by '-11'. r = -0.4545454545 Simplifying r = -0.4545454545Subproblem 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 = {-0.4545454545, 3}
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