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Simplifying 8d + 4(3 + -6d) + -12d = 5 + -1(4d + -7) 8d + (3 * 4 + -6d * 4) + -12d = 5 + -1(4d + -7) 8d + (12 + -24d) + -12d = 5 + -1(4d + -7) Reorder the terms: 12 + 8d + -24d + -12d = 5 + -1(4d + -7) Combine like terms: 8d + -24d = -16d 12 + -16d + -12d = 5 + -1(4d + -7) Combine like terms: -16d + -12d = -28d 12 + -28d = 5 + -1(4d + -7) Reorder the terms: 12 + -28d = 5 + -1(-7 + 4d) 12 + -28d = 5 + (-7 * -1 + 4d * -1) 12 + -28d = 5 + (7 + -4d) Combine like terms: 5 + 7 = 12 12 + -28d = 12 + -4d Add '-12' to each side of the equation. 12 + -12 + -28d = 12 + -12 + -4d Combine like terms: 12 + -12 = 0 0 + -28d = 12 + -12 + -4d -28d = 12 + -12 + -4d Combine like terms: 12 + -12 = 0 -28d = 0 + -4d -28d = -4d Solving -28d = -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. -28d + 4d = -4d + 4d Combine like terms: -28d + 4d = -24d -24d = -4d + 4d Combine like terms: -4d + 4d = 0 -24d = 0 Divide each side by '-24'. d = 0 Simplifying d = 0
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