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Simplifying 5x(8y + -9z) + -8y(5d + -9z) = 0 (8y * 5x + -9z * 5x) + -8y(5d + -9z) = 0 (40xy + -45xz) + -8y(5d + -9z) = 0 40xy + -45xz + (5d * -8y + -9z * -8y) = 0 40xy + -45xz + (-40dy + 72yz) = 0 Reorder the terms: -40dy + 40xy + -45xz + 72yz = 0 Solving -40dy + 40xy + -45xz + 72yz = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-40xy' to each side of the equation. -40dy + 40xy + -45xz + -40xy + 72yz = 0 + -40xy Reorder the terms: -40dy + 40xy + -40xy + -45xz + 72yz = 0 + -40xy Combine like terms: 40xy + -40xy = 0 -40dy + 0 + -45xz + 72yz = 0 + -40xy -40dy + -45xz + 72yz = 0 + -40xy Remove the zero: -40dy + -45xz + 72yz = -40xy Add '45xz' to each side of the equation. -40dy + -45xz + 45xz + 72yz = -40xy + 45xz Combine like terms: -45xz + 45xz = 0 -40dy + 0 + 72yz = -40xy + 45xz -40dy + 72yz = -40xy + 45xz Add '-72yz' to each side of the equation. -40dy + 72yz + -72yz = -40xy + 45xz + -72yz Combine like terms: 72yz + -72yz = 0 -40dy + 0 = -40xy + 45xz + -72yz -40dy = -40xy + 45xz + -72yz Divide each side by '-40y'. d = x + -1.125xy-1z + 1.8z Simplifying d = x + -1.125xy-1z + 1.8z
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