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Simplifying 2(3k + 5) + -3(k + 2) = 0 Reorder the terms: 2(5 + 3k) + -3(k + 2) = 0 (5 * 2 + 3k * 2) + -3(k + 2) = 0 (10 + 6k) + -3(k + 2) = 0 Reorder the terms: 10 + 6k + -3(2 + k) = 0 10 + 6k + (2 * -3 + k * -3) = 0 10 + 6k + (-6 + -3k) = 0 Reorder the terms: 10 + -6 + 6k + -3k = 0 Combine like terms: 10 + -6 = 4 4 + 6k + -3k = 0 Combine like terms: 6k + -3k = 3k 4 + 3k = 0 Solving 4 + 3k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3k = 0 + -4 3k = 0 + -4 Combine like terms: 0 + -4 = -4 3k = -4 Divide each side by '3'. k = -1.333333333 Simplifying k = -1.333333333
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