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Simplifying 3(4d + 7) = 5d + -42 Reorder the terms: 3(7 + 4d) = 5d + -42 (7 * 3 + 4d * 3) = 5d + -42 (21 + 12d) = 5d + -42 Reorder the terms: 21 + 12d = -42 + 5d Solving 21 + 12d = -42 + 5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5d' to each side of the equation. 21 + 12d + -5d = -42 + 5d + -5d Combine like terms: 12d + -5d = 7d 21 + 7d = -42 + 5d + -5d Combine like terms: 5d + -5d = 0 21 + 7d = -42 + 0 21 + 7d = -42 Add '-21' to each side of the equation. 21 + -21 + 7d = -42 + -21 Combine like terms: 21 + -21 = 0 0 + 7d = -42 + -21 7d = -42 + -21 Combine like terms: -42 + -21 = -63 7d = -63 Divide each side by '7'. d = -9 Simplifying d = -9
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