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Simplifying 6r(5 + -7r) + -6r(1 + -3r) = 0 (5 * 6r + -7r * 6r) + -6r(1 + -3r) = 0 (30r + -42r2) + -6r(1 + -3r) = 0 30r + -42r2 + (1 * -6r + -3r * -6r) = 0 30r + -42r2 + (-6r + 18r2) = 0 Reorder the terms: 30r + -6r + -42r2 + 18r2 = 0 Combine like terms: 30r + -6r = 24r 24r + -42r2 + 18r2 = 0 Combine like terms: -42r2 + 18r2 = -24r2 24r + -24r2 = 0 Solving 24r + -24r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '24r'. 24r(1 + -1r) = 0 Ignore the factor 24.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 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, 1}
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