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Simplifying 17 + 5[8 + -6(3t + -5)] + 3(4t + -16) = 0 Reorder the terms: 17 + 5[8 + -6(-5 + 3t)] + 3(4t + -16) = 0 17 + 5[8 + (-5 * -6 + 3t * -6)] + 3(4t + -16) = 0 17 + 5[8 + (30 + -18t)] + 3(4t + -16) = 0 Combine like terms: 8 + 30 = 38 17 + 5[38 + -18t] + 3(4t + -16) = 0 17 + [38 * 5 + -18t * 5] + 3(4t + -16) = 0 17 + [190 + -90t] + 3(4t + -16) = 0 Reorder the terms: 17 + 190 + -90t + 3(-16 + 4t) = 0 17 + 190 + -90t + (-16 * 3 + 4t * 3) = 0 17 + 190 + -90t + (-48 + 12t) = 0 Reorder the terms: 17 + 190 + -48 + -90t + 12t = 0 Combine like terms: 17 + 190 = 207 207 + -48 + -90t + 12t = 0 Combine like terms: 207 + -48 = 159 159 + -90t + 12t = 0 Combine like terms: -90t + 12t = -78t 159 + -78t = 0 Solving 159 + -78t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-159' to each side of the equation. 159 + -159 + -78t = 0 + -159 Combine like terms: 159 + -159 = 0 0 + -78t = 0 + -159 -78t = 0 + -159 Combine like terms: 0 + -159 = -159 -78t = -159 Divide each side by '-78'. t = 2.038461538 Simplifying t = 2.038461538
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