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Simplifying 4(d + 3) + -2(d + 7) + 5 = 5(d + 12) Reorder the terms: 4(3 + d) + -2(d + 7) + 5 = 5(d + 12) (3 * 4 + d * 4) + -2(d + 7) + 5 = 5(d + 12) (12 + 4d) + -2(d + 7) + 5 = 5(d + 12) Reorder the terms: 12 + 4d + -2(7 + d) + 5 = 5(d + 12) 12 + 4d + (7 * -2 + d * -2) + 5 = 5(d + 12) 12 + 4d + (-14 + -2d) + 5 = 5(d + 12) Reorder the terms: 12 + -14 + 5 + 4d + -2d = 5(d + 12) Combine like terms: 12 + -14 = -2 -2 + 5 + 4d + -2d = 5(d + 12) Combine like terms: -2 + 5 = 3 3 + 4d + -2d = 5(d + 12) Combine like terms: 4d + -2d = 2d 3 + 2d = 5(d + 12) Reorder the terms: 3 + 2d = 5(12 + d) 3 + 2d = (12 * 5 + d * 5) 3 + 2d = (60 + 5d) Solving 3 + 2d = 60 + 5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5d' to each side of the equation. 3 + 2d + -5d = 60 + 5d + -5d Combine like terms: 2d + -5d = -3d 3 + -3d = 60 + 5d + -5d Combine like terms: 5d + -5d = 0 3 + -3d = 60 + 0 3 + -3d = 60 Add '-3' to each side of the equation. 3 + -3 + -3d = 60 + -3 Combine like terms: 3 + -3 = 0 0 + -3d = 60 + -3 -3d = 60 + -3 Combine like terms: 60 + -3 = 57 -3d = 57 Divide each side by '-3'. d = -19 Simplifying d = -19
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