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Simplifying (3r + -24)(24r + -3) = 0 Reorder the terms: (-24 + 3r)(24r + -3) = 0 Reorder the terms: (-24 + 3r)(-3 + 24r) = 0 Multiply (-24 + 3r) * (-3 + 24r) (-24(-3 + 24r) + 3r * (-3 + 24r)) = 0 ((-3 * -24 + 24r * -24) + 3r * (-3 + 24r)) = 0 ((72 + -576r) + 3r * (-3 + 24r)) = 0 (72 + -576r + (-3 * 3r + 24r * 3r)) = 0 (72 + -576r + (-9r + 72r2)) = 0 Combine like terms: -576r + -9r = -585r (72 + -585r + 72r2) = 0 Solving 72 + -585r + 72r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '9'. 9(8 + -65r + 8r2) = 0 Factor a trinomial. 9((1 + -8r)(8 + -1r)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -8r)' equal to zero and attempt to solve: Simplifying 1 + -8r = 0 Solving 1 + -8r = 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 + -8r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8r = 0 + -1 -8r = 0 + -1 Combine like terms: 0 + -1 = -1 -8r = -1 Divide each side by '-8'. r = 0.125 Simplifying r = 0.125Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 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 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8Solution
r = {0.125, 8}
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