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Simplifying 5(3d + e) + -4(d + -4e) = 0 (3d * 5 + e * 5) + -4(d + -4e) = 0 (15d + 5e) + -4(d + -4e) = 0 15d + 5e + (d * -4 + -4e * -4) = 0 15d + 5e + (-4d + 16e) = 0 Reorder the terms: 15d + -4d + 5e + 16e = 0 Combine like terms: 15d + -4d = 11d 11d + 5e + 16e = 0 Combine like terms: 5e + 16e = 21e 11d + 21e = 0 Solving 11d + 21e = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-21e' to each side of the equation. 11d + 21e + -21e = 0 + -21e Combine like terms: 21e + -21e = 0 11d + 0 = 0 + -21e 11d = 0 + -21e Remove the zero: 11d = -21e Divide each side by '11'. d = -1.909090909e Simplifying d = -1.909090909e
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