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Simplifying 9 + 2d(4d + 1) + -5d = 7 + -8d(1 + -1d) Reorder the terms: 9 + 2d(1 + 4d) + -5d = 7 + -8d(1 + -1d) 9 + (1 * 2d + 4d * 2d) + -5d = 7 + -8d(1 + -1d) 9 + (2d + 8d2) + -5d = 7 + -8d(1 + -1d) Reorder the terms: 9 + 2d + -5d + 8d2 = 7 + -8d(1 + -1d) Combine like terms: 2d + -5d = -3d 9 + -3d + 8d2 = 7 + -8d(1 + -1d) 9 + -3d + 8d2 = 7 + (1 * -8d + -1d * -8d) 9 + -3d + 8d2 = 7 + (-8d + 8d2) Add '-8d2' to each side of the equation. 9 + -3d + 8d2 + -8d2 = 7 + -8d + 8d2 + -8d2 Combine like terms: 8d2 + -8d2 = 0 9 + -3d + 0 = 7 + -8d + 8d2 + -8d2 9 + -3d = 7 + -8d + 8d2 + -8d2 Combine like terms: 8d2 + -8d2 = 0 9 + -3d = 7 + -8d + 0 9 + -3d = 7 + -8d Solving 9 + -3d = 7 + -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. 9 + -3d + 8d = 7 + -8d + 8d Combine like terms: -3d + 8d = 5d 9 + 5d = 7 + -8d + 8d Combine like terms: -8d + 8d = 0 9 + 5d = 7 + 0 9 + 5d = 7 Add '-9' to each side of the equation. 9 + -9 + 5d = 7 + -9 Combine like terms: 9 + -9 = 0 0 + 5d = 7 + -9 5d = 7 + -9 Combine like terms: 7 + -9 = -2 5d = -2 Divide each side by '5'. d = -0.4 Simplifying d = -0.4
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