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Simplifying 3[d + 2(f + -3) + -4(f + -6d)] = 0 Reorder the terms: 3[d + 2(-3 + f) + -4(f + -6d)] = 0 3[d + (-3 * 2 + f * 2) + -4(f + -6d)] = 0 3[d + (-6 + 2f) + -4(f + -6d)] = 0 Reorder the terms: 3[d + -6 + 2f + -4(-6d + f)] = 0 3[d + -6 + 2f + (-6d * -4 + f * -4)] = 0 3[d + -6 + 2f + (24d + -4f)] = 0 Reorder the terms: 3[-6 + d + 24d + 2f + -4f] = 0 Combine like terms: d + 24d = 25d 3[-6 + 25d + 2f + -4f] = 0 Combine like terms: 2f + -4f = -2f 3[-6 + 25d + -2f] = 0 [-6 * 3 + 25d * 3 + -2f * 3] = 0 [-18 + 75d + -6f] = 0 Solving -18 + 75d + -6f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 75d + 18 + -6f = 0 + 18 Reorder the terms: -18 + 18 + 75d + -6f = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 75d + -6f = 0 + 18 75d + -6f = 0 + 18 Combine like terms: 0 + 18 = 18 75d + -6f = 18 Add '6f' to each side of the equation. 75d + -6f + 6f = 18 + 6f Combine like terms: -6f + 6f = 0 75d + 0 = 18 + 6f 75d = 18 + 6f Divide each side by '75'. d = 0.24 + 0.08f Simplifying d = 0.24 + 0.08f
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