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Simplifying 4(4d + -5e + 2f) + -1(5f + -6e + 2d) = 0 (4d * 4 + -5e * 4 + 2f * 4) + -1(5f + -6e + 2d) = 0 (16d + -20e + 8f) + -1(5f + -6e + 2d) = 0 Reorder the terms: 16d + -20e + 8f + -1(2d + -6e + 5f) = 0 16d + -20e + 8f + (2d * -1 + -6e * -1 + 5f * -1) = 0 16d + -20e + 8f + (-2d + 6e + -5f) = 0 Reorder the terms: 16d + -2d + -20e + 6e + 8f + -5f = 0 Combine like terms: 16d + -2d = 14d 14d + -20e + 6e + 8f + -5f = 0 Combine like terms: -20e + 6e = -14e 14d + -14e + 8f + -5f = 0 Combine like terms: 8f + -5f = 3f 14d + -14e + 3f = 0 Solving 14d + -14e + 3f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14e' to each side of the equation. 14d + -14e + 14e + 3f = 0 + 14e Combine like terms: -14e + 14e = 0 14d + 0 + 3f = 0 + 14e 14d + 3f = 0 + 14e Remove the zero: 14d + 3f = 14e Add '-3f' to each side of the equation. 14d + 3f + -3f = 14e + -3f Combine like terms: 3f + -3f = 0 14d + 0 = 14e + -3f 14d = 14e + -3f Divide each side by '14'. d = e + -0.2142857143f Simplifying d = e + -0.2142857143f
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