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Simplifying 4(2d + 9) + 3d + -78 = 4d Reorder the terms: 4(9 + 2d) + 3d + -78 = 4d (9 * 4 + 2d * 4) + 3d + -78 = 4d (36 + 8d) + 3d + -78 = 4d Reorder the terms: 36 + -78 + 8d + 3d = 4d Combine like terms: 36 + -78 = -42 -42 + 8d + 3d = 4d Combine like terms: 8d + 3d = 11d -42 + 11d = 4d Solving -42 + 11d = 4d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4d' to each side of the equation. -42 + 11d + -4d = 4d + -4d Combine like terms: 11d + -4d = 7d -42 + 7d = 4d + -4d Combine like terms: 4d + -4d = 0 -42 + 7d = 0 Add '42' to each side of the equation. -42 + 42 + 7d = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 7d = 0 + 42 7d = 0 + 42 Combine like terms: 0 + 42 = 42 7d = 42 Divide each side by '7'. d = 6 Simplifying d = 6
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