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Simplifying 3(3t + 4d) + 4(5t + -3d) = 0 Reorder the terms: 3(4d + 3t) + 4(5t + -3d) = 0 (4d * 3 + 3t * 3) + 4(5t + -3d) = 0 (12d + 9t) + 4(5t + -3d) = 0 Reorder the terms: 12d + 9t + 4(-3d + 5t) = 0 12d + 9t + (-3d * 4 + 5t * 4) = 0 12d + 9t + (-12d + 20t) = 0 Reorder the terms: 12d + -12d + 9t + 20t = 0 Combine like terms: 12d + -12d = 0 0 + 9t + 20t = 0 9t + 20t = 0 Combine like terms: 9t + 20t = 29t 29t = 0 Solving 29t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Divide each side by '29'. t = 0 Simplifying t = 0
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