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Simplifying (5r + -4s + 6) + (12r + -6s + -5) = 0 Reorder the terms: (6 + 5r + -4s) + (12r + -6s + -5) = 0 Remove parenthesis around (6 + 5r + -4s) 6 + 5r + -4s + (12r + -6s + -5) = 0 Reorder the terms: 6 + 5r + -4s + (-5 + 12r + -6s) = 0 Remove parenthesis around (-5 + 12r + -6s) 6 + 5r + -4s + -5 + 12r + -6s = 0 Reorder the terms: 6 + -5 + 5r + 12r + -4s + -6s = 0 Combine like terms: 6 + -5 = 1 1 + 5r + 12r + -4s + -6s = 0 Combine like terms: 5r + 12r = 17r 1 + 17r + -4s + -6s = 0 Combine like terms: -4s + -6s = -10s 1 + 17r + -10s = 0 Solving 1 + 17r + -10s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 17r + -1 + -10s = 0 + -1 Reorder the terms: 1 + -1 + 17r + -10s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 17r + -10s = 0 + -1 17r + -10s = 0 + -1 Combine like terms: 0 + -1 = -1 17r + -10s = -1 Add '10s' to each side of the equation. 17r + -10s + 10s = -1 + 10s Combine like terms: -10s + 10s = 0 17r + 0 = -1 + 10s 17r = -1 + 10s Divide each side by '17'. r = -0.05882352941 + 0.5882352941s Simplifying r = -0.05882352941 + 0.5882352941s
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