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Simplifying (5r + -4)(6r + -6) = 0 Reorder the terms: (-4 + 5r)(6r + -6) = 0 Reorder the terms: (-4 + 5r)(-6 + 6r) = 0 Multiply (-4 + 5r) * (-6 + 6r) (-4(-6 + 6r) + 5r * (-6 + 6r)) = 0 ((-6 * -4 + 6r * -4) + 5r * (-6 + 6r)) = 0 ((24 + -24r) + 5r * (-6 + 6r)) = 0 (24 + -24r + (-6 * 5r + 6r * 5r)) = 0 (24 + -24r + (-30r + 30r2)) = 0 Combine like terms: -24r + -30r = -54r (24 + -54r + 30r2) = 0 Solving 24 + -54r + 30r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -9r + 5r2) = 0 Factor a trinomial. 6((4 + -5r)(1 + -1r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -5r)' equal to zero and attempt to solve: Simplifying 4 + -5r = 0 Solving 4 + -5r = 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 + -5r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5r = 0 + -4 -5r = 0 + -4 Combine like terms: 0 + -4 = -4 -5r = -4 Divide each side by '-5'. r = 0.8 Simplifying r = 0.8Subproblem 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 = {0.8, 1}
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