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Simplifying 5(3k + 4m) + -4(3k + -2m) = 0 (3k * 5 + 4m * 5) + -4(3k + -2m) = 0 (15k + 20m) + -4(3k + -2m) = 0 15k + 20m + (3k * -4 + -2m * -4) = 0 15k + 20m + (-12k + 8m) = 0 Reorder the terms: 15k + -12k + 20m + 8m = 0 Combine like terms: 15k + -12k = 3k 3k + 20m + 8m = 0 Combine like terms: 20m + 8m = 28m 3k + 28m = 0 Solving 3k + 28m = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-28m' to each side of the equation. 3k + 28m + -28m = 0 + -28m Combine like terms: 28m + -28m = 0 3k + 0 = 0 + -28m 3k = 0 + -28m Remove the zero: 3k = -28m Divide each side by '3'. k = -9.333333333m Simplifying k = -9.333333333m
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