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Simplifying 5t + -3(2 + -7t) + 12 = 3t + -1(2 + t) 5t + (2 * -3 + -7t * -3) + 12 = 3t + -1(2 + t) 5t + (-6 + 21t) + 12 = 3t + -1(2 + t) Reorder the terms: -6 + 12 + 5t + 21t = 3t + -1(2 + t) Combine like terms: -6 + 12 = 6 6 + 5t + 21t = 3t + -1(2 + t) Combine like terms: 5t + 21t = 26t 6 + 26t = 3t + -1(2 + t) 6 + 26t = 3t + (2 * -1 + t * -1) 6 + 26t = 3t + (-2 + -1t) Reorder the terms: 6 + 26t = -2 + 3t + -1t Combine like terms: 3t + -1t = 2t 6 + 26t = -2 + 2t Solving 6 + 26t = -2 + 2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2t' to each side of the equation. 6 + 26t + -2t = -2 + 2t + -2t Combine like terms: 26t + -2t = 24t 6 + 24t = -2 + 2t + -2t Combine like terms: 2t + -2t = 0 6 + 24t = -2 + 0 6 + 24t = -2 Add '-6' to each side of the equation. 6 + -6 + 24t = -2 + -6 Combine like terms: 6 + -6 = 0 0 + 24t = -2 + -6 24t = -2 + -6 Combine like terms: -2 + -6 = -8 24t = -8 Divide each side by '24'. t = -0.3333333333 Simplifying t = -0.3333333333
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