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Simplifying 5(3t + 2) + 7(2t + 5) = 0 Reorder the terms: 5(2 + 3t) + 7(2t + 5) = 0 (2 * 5 + 3t * 5) + 7(2t + 5) = 0 (10 + 15t) + 7(2t + 5) = 0 Reorder the terms: 10 + 15t + 7(5 + 2t) = 0 10 + 15t + (5 * 7 + 2t * 7) = 0 10 + 15t + (35 + 14t) = 0 Reorder the terms: 10 + 35 + 15t + 14t = 0 Combine like terms: 10 + 35 = 45 45 + 15t + 14t = 0 Combine like terms: 15t + 14t = 29t 45 + 29t = 0 Solving 45 + 29t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 29t = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 29t = 0 + -45 29t = 0 + -45 Combine like terms: 0 + -45 = -45 29t = -45 Divide each side by '29'. t = -1.551724138 Simplifying t = -1.551724138
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