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Simplifying 4(5d + 8s + 20) + 3(4d + 5s + 10) = 0 Reorder the terms: 4(20 + 5d + 8s) + 3(4d + 5s + 10) = 0 (20 * 4 + 5d * 4 + 8s * 4) + 3(4d + 5s + 10) = 0 (80 + 20d + 32s) + 3(4d + 5s + 10) = 0 Reorder the terms: 80 + 20d + 32s + 3(10 + 4d + 5s) = 0 80 + 20d + 32s + (10 * 3 + 4d * 3 + 5s * 3) = 0 80 + 20d + 32s + (30 + 12d + 15s) = 0 Reorder the terms: 80 + 30 + 20d + 12d + 32s + 15s = 0 Combine like terms: 80 + 30 = 110 110 + 20d + 12d + 32s + 15s = 0 Combine like terms: 20d + 12d = 32d 110 + 32d + 32s + 15s = 0 Combine like terms: 32s + 15s = 47s 110 + 32d + 47s = 0 Solving 110 + 32d + 47s = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + 32d + -110 + 47s = 0 + -110 Reorder the terms: 110 + -110 + 32d + 47s = 0 + -110 Combine like terms: 110 + -110 = 0 0 + 32d + 47s = 0 + -110 32d + 47s = 0 + -110 Combine like terms: 0 + -110 = -110 32d + 47s = -110 Add '-47s' to each side of the equation. 32d + 47s + -47s = -110 + -47s Combine like terms: 47s + -47s = 0 32d + 0 = -110 + -47s 32d = -110 + -47s Divide each side by '32'. d = -3.4375 + -1.46875s Simplifying d = -3.4375 + -1.46875s
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