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Simplifying 4(2d + 1) + 6(9d + -2) = 3(5d + -4) + 4 Reorder the terms: 4(1 + 2d) + 6(9d + -2) = 3(5d + -4) + 4 (1 * 4 + 2d * 4) + 6(9d + -2) = 3(5d + -4) + 4 (4 + 8d) + 6(9d + -2) = 3(5d + -4) + 4 Reorder the terms: 4 + 8d + 6(-2 + 9d) = 3(5d + -4) + 4 4 + 8d + (-2 * 6 + 9d * 6) = 3(5d + -4) + 4 4 + 8d + (-12 + 54d) = 3(5d + -4) + 4 Reorder the terms: 4 + -12 + 8d + 54d = 3(5d + -4) + 4 Combine like terms: 4 + -12 = -8 -8 + 8d + 54d = 3(5d + -4) + 4 Combine like terms: 8d + 54d = 62d -8 + 62d = 3(5d + -4) + 4 Reorder the terms: -8 + 62d = 3(-4 + 5d) + 4 -8 + 62d = (-4 * 3 + 5d * 3) + 4 -8 + 62d = (-12 + 15d) + 4 Reorder the terms: -8 + 62d = -12 + 4 + 15d Combine like terms: -12 + 4 = -8 -8 + 62d = -8 + 15d Add '8' to each side of the equation. -8 + 8 + 62d = -8 + 8 + 15d Combine like terms: -8 + 8 = 0 0 + 62d = -8 + 8 + 15d 62d = -8 + 8 + 15d Combine like terms: -8 + 8 = 0 62d = 0 + 15d 62d = 15d Solving 62d = 15d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-15d' to each side of the equation. 62d + -15d = 15d + -15d Combine like terms: 62d + -15d = 47d 47d = 15d + -15d Combine like terms: 15d + -15d = 0 47d = 0 Divide each side by '47'. d = 0 Simplifying d = 0
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