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Simplifying 2(3t + 6) = -3[-3t + -3(t + -2)] Reorder the terms: 2(6 + 3t) = -3[-3t + -3(t + -2)] (6 * 2 + 3t * 2) = -3[-3t + -3(t + -2)] (12 + 6t) = -3[-3t + -3(t + -2)] Reorder the terms: 12 + 6t = -3[-3t + -3(-2 + t)] 12 + 6t = -3[-3t + (-2 * -3 + t * -3)] 12 + 6t = -3[-3t + (6 + -3t)] Reorder the terms: 12 + 6t = -3[6 + -3t + -3t] Combine like terms: -3t + -3t = -6t 12 + 6t = -3[6 + -6t] 12 + 6t = [6 * -3 + -6t * -3] 12 + 6t = [-18 + 18t] Solving 12 + 6t = -18 + 18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-18t' to each side of the equation. 12 + 6t + -18t = -18 + 18t + -18t Combine like terms: 6t + -18t = -12t 12 + -12t = -18 + 18t + -18t Combine like terms: 18t + -18t = 0 12 + -12t = -18 + 0 12 + -12t = -18 Add '-12' to each side of the equation. 12 + -12 + -12t = -18 + -12 Combine like terms: 12 + -12 = 0 0 + -12t = -18 + -12 -12t = -18 + -12 Combine like terms: -18 + -12 = -30 -12t = -30 Divide each side by '-12'. t = 2.5 Simplifying t = 2.5
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