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Simplifying -5(7 + -4d) + 6(4f + -7) = 0 (7 * -5 + -4d * -5) + 6(4f + -7) = 0 (-35 + 20d) + 6(4f + -7) = 0 Reorder the terms: -35 + 20d + 6(-7 + 4f) = 0 -35 + 20d + (-7 * 6 + 4f * 6) = 0 -35 + 20d + (-42 + 24f) = 0 Reorder the terms: -35 + -42 + 20d + 24f = 0 Combine like terms: -35 + -42 = -77 -77 + 20d + 24f = 0 Solving -77 + 20d + 24f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '77' to each side of the equation. -77 + 20d + 77 + 24f = 0 + 77 Reorder the terms: -77 + 77 + 20d + 24f = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 20d + 24f = 0 + 77 20d + 24f = 0 + 77 Combine like terms: 0 + 77 = 77 20d + 24f = 77 Add '-24f' to each side of the equation. 20d + 24f + -24f = 77 + -24f Combine like terms: 24f + -24f = 0 20d + 0 = 77 + -24f 20d = 77 + -24f Divide each side by '20'. d = 3.85 + -1.2f Simplifying d = 3.85 + -1.2f
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