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Simplifying 12(t + 6) + 8 = 4(2t + -1) + 2t Reorder the terms: 12(6 + t) + 8 = 4(2t + -1) + 2t (6 * 12 + t * 12) + 8 = 4(2t + -1) + 2t (72 + 12t) + 8 = 4(2t + -1) + 2t Reorder the terms: 72 + 8 + 12t = 4(2t + -1) + 2t Combine like terms: 72 + 8 = 80 80 + 12t = 4(2t + -1) + 2t Reorder the terms: 80 + 12t = 4(-1 + 2t) + 2t 80 + 12t = (-1 * 4 + 2t * 4) + 2t 80 + 12t = (-4 + 8t) + 2t Combine like terms: 8t + 2t = 10t 80 + 12t = -4 + 10t Solving 80 + 12t = -4 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 80 + 12t + -10t = -4 + 10t + -10t Combine like terms: 12t + -10t = 2t 80 + 2t = -4 + 10t + -10t Combine like terms: 10t + -10t = 0 80 + 2t = -4 + 0 80 + 2t = -4 Add '-80' to each side of the equation. 80 + -80 + 2t = -4 + -80 Combine like terms: 80 + -80 = 0 0 + 2t = -4 + -80 2t = -4 + -80 Combine like terms: -4 + -80 = -84 2t = -84 Divide each side by '2'. t = -42 Simplifying t = -42
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