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Simplifying 2(4t + 6) + -3(2t + -3) = -3(3t + -4) + 5 + -1t Reorder the terms: 2(6 + 4t) + -3(2t + -3) = -3(3t + -4) + 5 + -1t (6 * 2 + 4t * 2) + -3(2t + -3) = -3(3t + -4) + 5 + -1t (12 + 8t) + -3(2t + -3) = -3(3t + -4) + 5 + -1t Reorder the terms: 12 + 8t + -3(-3 + 2t) = -3(3t + -4) + 5 + -1t 12 + 8t + (-3 * -3 + 2t * -3) = -3(3t + -4) + 5 + -1t 12 + 8t + (9 + -6t) = -3(3t + -4) + 5 + -1t Reorder the terms: 12 + 9 + 8t + -6t = -3(3t + -4) + 5 + -1t Combine like terms: 12 + 9 = 21 21 + 8t + -6t = -3(3t + -4) + 5 + -1t Combine like terms: 8t + -6t = 2t 21 + 2t = -3(3t + -4) + 5 + -1t Reorder the terms: 21 + 2t = -3(-4 + 3t) + 5 + -1t 21 + 2t = (-4 * -3 + 3t * -3) + 5 + -1t 21 + 2t = (12 + -9t) + 5 + -1t Reorder the terms: 21 + 2t = 12 + 5 + -9t + -1t Combine like terms: 12 + 5 = 17 21 + 2t = 17 + -9t + -1t Combine like terms: -9t + -1t = -10t 21 + 2t = 17 + -10t Solving 21 + 2t = 17 + -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. 21 + 2t + 10t = 17 + -10t + 10t Combine like terms: 2t + 10t = 12t 21 + 12t = 17 + -10t + 10t Combine like terms: -10t + 10t = 0 21 + 12t = 17 + 0 21 + 12t = 17 Add '-21' to each side of the equation. 21 + -21 + 12t = 17 + -21 Combine like terms: 21 + -21 = 0 0 + 12t = 17 + -21 12t = 17 + -21 Combine like terms: 17 + -21 = -4 12t = -4 Divide each side by '12'. t = -0.3333333333 Simplifying t = -0.3333333333
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