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Simplifying 2[d + -1(4d + 9) + 3] = 2(d + 6) Reorder the terms: 2[d + -1(9 + 4d) + 3] = 2(d + 6) 2[d + (9 * -1 + 4d * -1) + 3] = 2(d + 6) 2[d + (-9 + -4d) + 3] = 2(d + 6) Reorder the terms: 2[-9 + 3 + d + -4d] = 2(d + 6) Combine like terms: -9 + 3 = -6 2[-6 + d + -4d] = 2(d + 6) Combine like terms: d + -4d = -3d 2[-6 + -3d] = 2(d + 6) [-6 * 2 + -3d * 2] = 2(d + 6) [-12 + -6d] = 2(d + 6) Reorder the terms: -12 + -6d = 2(6 + d) -12 + -6d = (6 * 2 + d * 2) -12 + -6d = (12 + 2d) Solving -12 + -6d = 12 + 2d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2d' to each side of the equation. -12 + -6d + -2d = 12 + 2d + -2d Combine like terms: -6d + -2d = -8d -12 + -8d = 12 + 2d + -2d Combine like terms: 2d + -2d = 0 -12 + -8d = 12 + 0 -12 + -8d = 12 Add '12' to each side of the equation. -12 + 12 + -8d = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -8d = 12 + 12 -8d = 12 + 12 Combine like terms: 12 + 12 = 24 -8d = 24 Divide each side by '-8'. d = -3 Simplifying d = -3
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