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Simplifying -5(1 + -5d) + 5(-8d + -2) = -4d + -8d (1 * -5 + -5d * -5) + 5(-8d + -2) = -4d + -8d (-5 + 25d) + 5(-8d + -2) = -4d + -8d Reorder the terms: -5 + 25d + 5(-2 + -8d) = -4d + -8d -5 + 25d + (-2 * 5 + -8d * 5) = -4d + -8d -5 + 25d + (-10 + -40d) = -4d + -8d Reorder the terms: -5 + -10 + 25d + -40d = -4d + -8d Combine like terms: -5 + -10 = -15 -15 + 25d + -40d = -4d + -8d Combine like terms: 25d + -40d = -15d -15 + -15d = -4d + -8d Combine like terms: -4d + -8d = -12d -15 + -15d = -12d Solving -15 + -15d = -12d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '12d' to each side of the equation. -15 + -15d + 12d = -12d + 12d Combine like terms: -15d + 12d = -3d -15 + -3d = -12d + 12d Combine like terms: -12d + 12d = 0 -15 + -3d = 0 Add '15' to each side of the equation. -15 + 15 + -3d = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3d = 0 + 15 -3d = 0 + 15 Combine like terms: 0 + 15 = 15 -3d = 15 Divide each side by '-3'. d = -5 Simplifying d = -5
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