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Simplifying 5(r + -6)(r + -5) = 0 Reorder the terms: 5(-6 + r)(r + -5) = 0 Reorder the terms: 5(-6 + r)(-5 + r) = 0 Multiply (-6 + r) * (-5 + r) 5(-6(-5 + r) + r(-5 + r)) = 0 5((-5 * -6 + r * -6) + r(-5 + r)) = 0 5((30 + -6r) + r(-5 + r)) = 0 5(30 + -6r + (-5 * r + r * r)) = 0 5(30 + -6r + (-5r + r2)) = 0 Combine like terms: -6r + -5r = -11r 5(30 + -11r + r2) = 0 (30 * 5 + -11r * 5 + r2 * 5) = 0 (150 + -55r + 5r2) = 0 Solving 150 + -55r + 5r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(30 + -11r + r2) = 0 Factor a trinomial. 5((5 + -1r)(6 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 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 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve: Simplifying 6 + -1r = 0 Solving 6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1r = 0 + -6 -1r = 0 + -6 Combine like terms: 0 + -6 = -6 -1r = -6 Divide each side by '-1'. r = 6 Simplifying r = 6Solution
r = {5, 6}
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