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Simplifying 5(2 + t) + 3(4t + 1) = 0 (2 * 5 + t * 5) + 3(4t + 1) = 0 (10 + 5t) + 3(4t + 1) = 0 Reorder the terms: 10 + 5t + 3(1 + 4t) = 0 10 + 5t + (1 * 3 + 4t * 3) = 0 10 + 5t + (3 + 12t) = 0 Reorder the terms: 10 + 3 + 5t + 12t = 0 Combine like terms: 10 + 3 = 13 13 + 5t + 12t = 0 Combine like terms: 5t + 12t = 17t 13 + 17t = 0 Solving 13 + 17t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 17t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 17t = 0 + -13 17t = 0 + -13 Combine like terms: 0 + -13 = -13 17t = -13 Divide each side by '17'. t = -0.7647058824 Simplifying t = -0.7647058824
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