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Simplifying 30d + -1(-1d + 6) + (-5d + 4) = (5d + 6) + (-8 + 3d) Reorder the terms: 30d + -1(6 + -1d) + (-5d + 4) = (5d + 6) + (-8 + 3d) 30d + (6 * -1 + -1d * -1) + (-5d + 4) = (5d + 6) + (-8 + 3d) 30d + (-6 + 1d) + (-5d + 4) = (5d + 6) + (-8 + 3d) Reorder the terms: 30d + -6 + 1d + (4 + -5d) = (5d + 6) + (-8 + 3d) Remove parenthesis around (4 + -5d) 30d + -6 + 1d + 4 + -5d = (5d + 6) + (-8 + 3d) Reorder the terms: -6 + 4 + 30d + 1d + -5d = (5d + 6) + (-8 + 3d) Combine like terms: -6 + 4 = -2 -2 + 30d + 1d + -5d = (5d + 6) + (-8 + 3d) Combine like terms: 30d + 1d = 31d -2 + 31d + -5d = (5d + 6) + (-8 + 3d) Combine like terms: 31d + -5d = 26d -2 + 26d = (5d + 6) + (-8 + 3d) Reorder the terms: -2 + 26d = (6 + 5d) + (-8 + 3d) Remove parenthesis around (6 + 5d) -2 + 26d = 6 + 5d + (-8 + 3d) Remove parenthesis around (-8 + 3d) -2 + 26d = 6 + 5d + -8 + 3d Reorder the terms: -2 + 26d = 6 + -8 + 5d + 3d Combine like terms: 6 + -8 = -2 -2 + 26d = -2 + 5d + 3d Combine like terms: 5d + 3d = 8d -2 + 26d = -2 + 8d Add '2' to each side of the equation. -2 + 2 + 26d = -2 + 2 + 8d Combine like terms: -2 + 2 = 0 0 + 26d = -2 + 2 + 8d 26d = -2 + 2 + 8d Combine like terms: -2 + 2 = 0 26d = 0 + 8d 26d = 8d Solving 26d = 8d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8d' to each side of the equation. 26d + -8d = 8d + -8d Combine like terms: 26d + -8d = 18d 18d = 8d + -8d Combine like terms: 8d + -8d = 0 18d = 0 Divide each side by '18'. d = 0 Simplifying d = 0
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