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Simplifying 8t + 4r + -7r + 9t + 3t + 6r = 0 Reorder the terms: 4r + -7r + 6r + 8t + 9t + 3t = 0 Combine like terms: 4r + -7r = -3r -3r + 6r + 8t + 9t + 3t = 0 Combine like terms: -3r + 6r = 3r 3r + 8t + 9t + 3t = 0 Combine like terms: 8t + 9t = 17t 3r + 17t + 3t = 0 Combine like terms: 17t + 3t = 20t 3r + 20t = 0 Solving 3r + 20t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20t' to each side of the equation. 3r + 20t + -20t = 0 + -20t Combine like terms: 20t + -20t = 0 3r + 0 = 0 + -20t 3r = 0 + -20t Remove the zero: 3r = -20t Divide each side by '3'. r = -6.666666667t Simplifying r = -6.666666667t
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