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Simplifying 4(t + 1) + -7(2t + -5) + 5(8t + 1) = 0 Reorder the terms: 4(1 + t) + -7(2t + -5) + 5(8t + 1) = 0 (1 * 4 + t * 4) + -7(2t + -5) + 5(8t + 1) = 0 (4 + 4t) + -7(2t + -5) + 5(8t + 1) = 0 Reorder the terms: 4 + 4t + -7(-5 + 2t) + 5(8t + 1) = 0 4 + 4t + (-5 * -7 + 2t * -7) + 5(8t + 1) = 0 4 + 4t + (35 + -14t) + 5(8t + 1) = 0 Reorder the terms: 4 + 4t + 35 + -14t + 5(1 + 8t) = 0 4 + 4t + 35 + -14t + (1 * 5 + 8t * 5) = 0 4 + 4t + 35 + -14t + (5 + 40t) = 0 Reorder the terms: 4 + 35 + 5 + 4t + -14t + 40t = 0 Combine like terms: 4 + 35 = 39 39 + 5 + 4t + -14t + 40t = 0 Combine like terms: 39 + 5 = 44 44 + 4t + -14t + 40t = 0 Combine like terms: 4t + -14t = -10t 44 + -10t + 40t = 0 Combine like terms: -10t + 40t = 30t 44 + 30t = 0 Solving 44 + 30t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + 30t = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 30t = 0 + -44 30t = 0 + -44 Combine like terms: 0 + -44 = -44 30t = -44 Divide each side by '30'. t = -1.466666667 Simplifying t = -1.466666667
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