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Simplifying 3(4d + -5) + 12d = -3d + -1(2d + -4) * 8 Reorder the terms: 3(-5 + 4d) + 12d = -3d + -1(2d + -4) * 8 (-5 * 3 + 4d * 3) + 12d = -3d + -1(2d + -4) * 8 (-15 + 12d) + 12d = -3d + -1(2d + -4) * 8 Combine like terms: 12d + 12d = 24d -15 + 24d = -3d + -1(2d + -4) * 8 Reorder the terms: -15 + 24d = -3d + -1(-4 + 2d) * 8 Reorder the terms for easier multiplication: -15 + 24d = -3d + -1 * 8(-4 + 2d) Multiply -1 * 8 -15 + 24d = -3d + -8(-4 + 2d) -15 + 24d = -3d + (-4 * -8 + 2d * -8) -15 + 24d = -3d + (32 + -16d) Reorder the terms: -15 + 24d = 32 + -3d + -16d Combine like terms: -3d + -16d = -19d -15 + 24d = 32 + -19d Solving -15 + 24d = 32 + -19d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '19d' to each side of the equation. -15 + 24d + 19d = 32 + -19d + 19d Combine like terms: 24d + 19d = 43d -15 + 43d = 32 + -19d + 19d Combine like terms: -19d + 19d = 0 -15 + 43d = 32 + 0 -15 + 43d = 32 Add '15' to each side of the equation. -15 + 15 + 43d = 32 + 15 Combine like terms: -15 + 15 = 0 0 + 43d = 32 + 15 43d = 32 + 15 Combine like terms: 32 + 15 = 47 43d = 47 Divide each side by '43'. d = 1.093023256 Simplifying d = 1.093023256
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