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Simplifying 7(3r + -2w) + 3(5r + 3w) = 0 (3r * 7 + -2w * 7) + 3(5r + 3w) = 0 (21r + -14w) + 3(5r + 3w) = 0 21r + -14w + (5r * 3 + 3w * 3) = 0 21r + -14w + (15r + 9w) = 0 Reorder the terms: 21r + 15r + -14w + 9w = 0 Combine like terms: 21r + 15r = 36r 36r + -14w + 9w = 0 Combine like terms: -14w + 9w = -5w 36r + -5w = 0 Solving 36r + -5w = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5w' to each side of the equation. 36r + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 36r + 0 = 0 + 5w 36r = 0 + 5w Remove the zero: 36r = 5w Divide each side by '36'. r = 0.1388888889w Simplifying r = 0.1388888889w
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