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Simplifying 33 + -1(5d + 6) = 12 + -6(d + 1) Reorder the terms: 33 + -1(6 + 5d) = 12 + -6(d + 1) 33 + (6 * -1 + 5d * -1) = 12 + -6(d + 1) 33 + (-6 + -5d) = 12 + -6(d + 1) Combine like terms: 33 + -6 = 27 27 + -5d = 12 + -6(d + 1) Reorder the terms: 27 + -5d = 12 + -6(1 + d) 27 + -5d = 12 + (1 * -6 + d * -6) 27 + -5d = 12 + (-6 + -6d) Combine like terms: 12 + -6 = 6 27 + -5d = 6 + -6d Solving 27 + -5d = 6 + -6d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6d' to each side of the equation. 27 + -5d + 6d = 6 + -6d + 6d Combine like terms: -5d + 6d = 1d 27 + 1d = 6 + -6d + 6d Combine like terms: -6d + 6d = 0 27 + 1d = 6 + 0 27 + 1d = 6 Add '-27' to each side of the equation. 27 + -27 + 1d = 6 + -27 Combine like terms: 27 + -27 = 0 0 + 1d = 6 + -27 1d = 6 + -27 Combine like terms: 6 + -27 = -21 1d = -21 Divide each side by '1'. d = -21 Simplifying d = -21
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