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Simplifying 5(2d + 9) = 3(3d + 13) Reorder the terms: 5(9 + 2d) = 3(3d + 13) (9 * 5 + 2d * 5) = 3(3d + 13) (45 + 10d) = 3(3d + 13) Reorder the terms: 45 + 10d = 3(13 + 3d) 45 + 10d = (13 * 3 + 3d * 3) 45 + 10d = (39 + 9d) Solving 45 + 10d = 39 + 9d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-9d' to each side of the equation. 45 + 10d + -9d = 39 + 9d + -9d Combine like terms: 10d + -9d = 1d 45 + 1d = 39 + 9d + -9d Combine like terms: 9d + -9d = 0 45 + 1d = 39 + 0 45 + 1d = 39 Add '-45' to each side of the equation. 45 + -45 + 1d = 39 + -45 Combine like terms: 45 + -45 = 0 0 + 1d = 39 + -45 1d = 39 + -45 Combine like terms: 39 + -45 = -6 1d = -6 Divide each side by '1'. d = -6 Simplifying d = -6
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