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Simplifying -2(t + 3) + 2(3t + -3) = 3(t + -1) + 3 Reorder the terms: -2(3 + t) + 2(3t + -3) = 3(t + -1) + 3 (3 * -2 + t * -2) + 2(3t + -3) = 3(t + -1) + 3 (-6 + -2t) + 2(3t + -3) = 3(t + -1) + 3 Reorder the terms: -6 + -2t + 2(-3 + 3t) = 3(t + -1) + 3 -6 + -2t + (-3 * 2 + 3t * 2) = 3(t + -1) + 3 -6 + -2t + (-6 + 6t) = 3(t + -1) + 3 Reorder the terms: -6 + -6 + -2t + 6t = 3(t + -1) + 3 Combine like terms: -6 + -6 = -12 -12 + -2t + 6t = 3(t + -1) + 3 Combine like terms: -2t + 6t = 4t -12 + 4t = 3(t + -1) + 3 Reorder the terms: -12 + 4t = 3(-1 + t) + 3 -12 + 4t = (-1 * 3 + t * 3) + 3 -12 + 4t = (-3 + 3t) + 3 Reorder the terms: -12 + 4t = -3 + 3 + 3t Combine like terms: -3 + 3 = 0 -12 + 4t = 0 + 3t -12 + 4t = 3t Solving -12 + 4t = 3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3t' to each side of the equation. -12 + 4t + -3t = 3t + -3t Combine like terms: 4t + -3t = 1t -12 + 1t = 3t + -3t Combine like terms: 3t + -3t = 0 -12 + 1t = 0 Add '12' to each side of the equation. -12 + 12 + 1t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1t = 0 + 12 1t = 0 + 12 Combine like terms: 0 + 12 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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