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Simplifying 6(2t + u) + -1(5t + -3u) = 0 (2t * 6 + u * 6) + -1(5t + -3u) = 0 (12t + 6u) + -1(5t + -3u) = 0 12t + 6u + (5t * -1 + -3u * -1) = 0 12t + 6u + (-5t + 3u) = 0 Reorder the terms: 12t + -5t + 6u + 3u = 0 Combine like terms: 12t + -5t = 7t 7t + 6u + 3u = 0 Combine like terms: 6u + 3u = 9u 7t + 9u = 0 Solving 7t + 9u = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9u' to each side of the equation. 7t + 9u + -9u = 0 + -9u Combine like terms: 9u + -9u = 0 7t + 0 = 0 + -9u 7t = 0 + -9u Remove the zero: 7t = -9u Divide each side by '7'. t = -1.285714286u Simplifying t = -1.285714286u
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