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Simplifying -30 = 5(4d + -7) + -1(7d + -5) Reorder the terms: -30 = 5(-7 + 4d) + -1(7d + -5) -30 = (-7 * 5 + 4d * 5) + -1(7d + -5) -30 = (-35 + 20d) + -1(7d + -5) Reorder the terms: -30 = -35 + 20d + -1(-5 + 7d) -30 = -35 + 20d + (-5 * -1 + 7d * -1) -30 = -35 + 20d + (5 + -7d) Reorder the terms: -30 = -35 + 5 + 20d + -7d Combine like terms: -35 + 5 = -30 -30 = -30 + 20d + -7d Combine like terms: 20d + -7d = 13d -30 = -30 + 13d Add '30' to each side of the equation. -30 + 30 = -30 + 30 + 13d Combine like terms: -30 + 30 = 0 0 = -30 + 30 + 13d Combine like terms: -30 + 30 = 0 0 = 0 + 13d 0 = 13d Solving 0 = 13d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-13d' to each side of the equation. 0 + -13d = 13d + -13d Remove the zero: -13d = 13d + -13d Combine like terms: 13d + -13d = 0 -13d = 0 Divide each side by '-13'. d = 0 Simplifying d = 0
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