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Simplifying 4(d + 3) + -3(d + -4) + 5(d + 6) = 96 Reorder the terms: 4(3 + d) + -3(d + -4) + 5(d + 6) = 96 (3 * 4 + d * 4) + -3(d + -4) + 5(d + 6) = 96 (12 + 4d) + -3(d + -4) + 5(d + 6) = 96 Reorder the terms: 12 + 4d + -3(-4 + d) + 5(d + 6) = 96 12 + 4d + (-4 * -3 + d * -3) + 5(d + 6) = 96 12 + 4d + (12 + -3d) + 5(d + 6) = 96 Reorder the terms: 12 + 4d + 12 + -3d + 5(6 + d) = 96 12 + 4d + 12 + -3d + (6 * 5 + d * 5) = 96 12 + 4d + 12 + -3d + (30 + 5d) = 96 Reorder the terms: 12 + 12 + 30 + 4d + -3d + 5d = 96 Combine like terms: 12 + 12 = 24 24 + 30 + 4d + -3d + 5d = 96 Combine like terms: 24 + 30 = 54 54 + 4d + -3d + 5d = 96 Combine like terms: 4d + -3d = 1d 54 + 1d + 5d = 96 Combine like terms: 1d + 5d = 6d 54 + 6d = 96 Solving 54 + 6d = 96 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + 6d = 96 + -54 Combine like terms: 54 + -54 = 0 0 + 6d = 96 + -54 6d = 96 + -54 Combine like terms: 96 + -54 = 42 6d = 42 Divide each side by '6'. d = 7 Simplifying d = 7
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