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Simplifying (4r + -3)(5r + -5) = 0 Reorder the terms: (-3 + 4r)(5r + -5) = 0 Reorder the terms: (-3 + 4r)(-5 + 5r) = 0 Multiply (-3 + 4r) * (-5 + 5r) (-3(-5 + 5r) + 4r * (-5 + 5r)) = 0 ((-5 * -3 + 5r * -3) + 4r * (-5 + 5r)) = 0 ((15 + -15r) + 4r * (-5 + 5r)) = 0 (15 + -15r + (-5 * 4r + 5r * 4r)) = 0 (15 + -15r + (-20r + 20r2)) = 0 Combine like terms: -15r + -20r = -35r (15 + -35r + 20r2) = 0 Solving 15 + -35r + 20r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -7r + 4r2) = 0 Factor a trinomial. 5((3 + -4r)(1 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -4r)' equal to zero and attempt to solve: Simplifying 3 + -4r = 0 Solving 3 + -4r = 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 + -4r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4r = 0 + -3 -4r = 0 + -3 Combine like terms: 0 + -3 = -3 -4r = -3 Divide each side by '-4'. r = 0.75 Simplifying r = 0.75Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {0.75, 1}
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