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Simplifying 3(2d + 7) + -6(d + 2) = -1d + -5(d + -3) Reorder the terms: 3(7 + 2d) + -6(d + 2) = -1d + -5(d + -3) (7 * 3 + 2d * 3) + -6(d + 2) = -1d + -5(d + -3) (21 + 6d) + -6(d + 2) = -1d + -5(d + -3) Reorder the terms: 21 + 6d + -6(2 + d) = -1d + -5(d + -3) 21 + 6d + (2 * -6 + d * -6) = -1d + -5(d + -3) 21 + 6d + (-12 + -6d) = -1d + -5(d + -3) Reorder the terms: 21 + -12 + 6d + -6d = -1d + -5(d + -3) Combine like terms: 21 + -12 = 9 9 + 6d + -6d = -1d + -5(d + -3) Combine like terms: 6d + -6d = 0 9 + 0 = -1d + -5(d + -3) 9 = -1d + -5(d + -3) Reorder the terms: 9 = -1d + -5(-3 + d) 9 = -1d + (-3 * -5 + d * -5) 9 = -1d + (15 + -5d) Reorder the terms: 9 = 15 + -1d + -5d Combine like terms: -1d + -5d = -6d 9 = 15 + -6d Solving 9 = 15 + -6d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6d' to each side of the equation. 9 + 6d = 15 + -6d + 6d Combine like terms: -6d + 6d = 0 9 + 6d = 15 + 0 9 + 6d = 15 Add '-9' to each side of the equation. 9 + -9 + 6d = 15 + -9 Combine like terms: 9 + -9 = 0 0 + 6d = 15 + -9 6d = 15 + -9 Combine like terms: 15 + -9 = 6 6d = 6 Divide each side by '6'. d = 1 Simplifying d = 1
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