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Simplifying 2 + [2 + 3(3d + -5(4 + -3d + 8) + -2)] = 3d + -2 Reorder the terms: 2 + [2 + 3(3d + -5(4 + 8 + -3d) + -2)] = 3d + -2 Combine like terms: 4 + 8 = 12 2 + [2 + 3(3d + -5(12 + -3d) + -2)] = 3d + -2 2 + [2 + 3(3d + (12 * -5 + -3d * -5) + -2)] = 3d + -2 2 + [2 + 3(3d + (-60 + 15d) + -2)] = 3d + -2 Reorder the terms: 2 + [2 + 3(-60 + -2 + 3d + 15d)] = 3d + -2 Combine like terms: -60 + -2 = -62 2 + [2 + 3(-62 + 3d + 15d)] = 3d + -2 Combine like terms: 3d + 15d = 18d 2 + [2 + 3(-62 + 18d)] = 3d + -2 2 + [2 + (-62 * 3 + 18d * 3)] = 3d + -2 2 + [2 + (-186 + 54d)] = 3d + -2 Combine like terms: 2 + -186 = -184 2 + [-184 + 54d] = 3d + -2 Remove brackets around [-184 + 54d] 2 + -184 + 54d = 3d + -2 Combine like terms: 2 + -184 = -182 -182 + 54d = 3d + -2 Reorder the terms: -182 + 54d = -2 + 3d Solving -182 + 54d = -2 + 3d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3d' to each side of the equation. -182 + 54d + -3d = -2 + 3d + -3d Combine like terms: 54d + -3d = 51d -182 + 51d = -2 + 3d + -3d Combine like terms: 3d + -3d = 0 -182 + 51d = -2 + 0 -182 + 51d = -2 Add '182' to each side of the equation. -182 + 182 + 51d = -2 + 182 Combine like terms: -182 + 182 = 0 0 + 51d = -2 + 182 51d = -2 + 182 Combine like terms: -2 + 182 = 180 51d = 180 Divide each side by '51'. d = 3.529411765 Simplifying d = 3.529411765
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