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Simplifying (11r + 8)(3r + -5) = 0 Reorder the terms: (8 + 11r)(3r + -5) = 0 Reorder the terms: (8 + 11r)(-5 + 3r) = 0 Multiply (8 + 11r) * (-5 + 3r) (8(-5 + 3r) + 11r * (-5 + 3r)) = 0 ((-5 * 8 + 3r * 8) + 11r * (-5 + 3r)) = 0 ((-40 + 24r) + 11r * (-5 + 3r)) = 0 (-40 + 24r + (-5 * 11r + 3r * 11r)) = 0 (-40 + 24r + (-55r + 33r2)) = 0 Combine like terms: 24r + -55r = -31r (-40 + -31r + 33r2) = 0 Solving -40 + -31r + 33r2 = 0 Solving for variable 'r'. Factor a trinomial. (-8 + -11r)(5 + -3r) = 0Subproblem 1
Set the factor '(-8 + -11r)' equal to zero and attempt to solve: Simplifying -8 + -11r = 0 Solving -8 + -11r = 0 Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -11r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -11r = 0 + 8 -11r = 0 + 8 Combine like terms: 0 + 8 = 8 -11r = 8 Divide each side by '-11'. r = -0.7272727273 Simplifying r = -0.7272727273Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 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 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {-0.7272727273, 1.666666667}
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