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Simplifying 3(t + 6) + 5(4t + 7) = 0 Reorder the terms: 3(6 + t) + 5(4t + 7) = 0 (6 * 3 + t * 3) + 5(4t + 7) = 0 (18 + 3t) + 5(4t + 7) = 0 Reorder the terms: 18 + 3t + 5(7 + 4t) = 0 18 + 3t + (7 * 5 + 4t * 5) = 0 18 + 3t + (35 + 20t) = 0 Reorder the terms: 18 + 35 + 3t + 20t = 0 Combine like terms: 18 + 35 = 53 53 + 3t + 20t = 0 Combine like terms: 3t + 20t = 23t 53 + 23t = 0 Solving 53 + 23t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + 23t = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 23t = 0 + -53 23t = 0 + -53 Combine like terms: 0 + -53 = -53 23t = -53 Divide each side by '23'. t = -2.304347826 Simplifying t = -2.304347826
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