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Simplifying d(5e + 2f) + -4d(e + 4b) = 0 (5e * d + 2f * d) + -4d(e + 4b) = 0 (5de + 2df) + -4d(e + 4b) = 0 Reorder the terms: 5de + 2df + -4d(4b + e) = 0 5de + 2df + (4b * -4d + e * -4d) = 0 5de + 2df + (-16bd + -4de) = 0 Reorder the terms: -16bd + 5de + -4de + 2df = 0 Combine like terms: 5de + -4de = 1de -16bd + 1de + 2df = 0 Solving -16bd + 1de + 2df = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1de' to each side of the equation. -16bd + 1de + -1de + 2df = 0 + -1de Combine like terms: 1de + -1de = 0 -16bd + 0 + 2df = 0 + -1de -16bd + 2df = 0 + -1de Remove the zero: -16bd + 2df = -1de Add '-2df' to each side of the equation. -16bd + 2df + -2df = -1de + -2df Combine like terms: 2df + -2df = 0 -16bd + 0 = -1de + -2df -16bd = -1de + -2df Divide each side by '-16d'. b = 0.0625e + 0.125f Simplifying b = 0.0625e + 0.125f
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