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Simplifying (12 + -3 + 5k) * 6 + 4k + -2(k + 5) = 0 Combine like terms: 12 + -3 = 9 (9 + 5k) * 6 + 4k + -2(k + 5) = 0 Reorder the terms for easier multiplication: 6(9 + 5k) + 4k + -2(k + 5) = 0 (9 * 6 + 5k * 6) + 4k + -2(k + 5) = 0 (54 + 30k) + 4k + -2(k + 5) = 0 Reorder the terms: 54 + 30k + 4k + -2(5 + k) = 0 54 + 30k + 4k + (5 * -2 + k * -2) = 0 54 + 30k + 4k + (-10 + -2k) = 0 Reorder the terms: 54 + -10 + 30k + 4k + -2k = 0 Combine like terms: 54 + -10 = 44 44 + 30k + 4k + -2k = 0 Combine like terms: 30k + 4k = 34k 44 + 34k + -2k = 0 Combine like terms: 34k + -2k = 32k 44 + 32k = 0 Solving 44 + 32k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + 32k = 0 + -44 Combine like terms: 44 + -44 = 0 0 + 32k = 0 + -44 32k = 0 + -44 Combine like terms: 0 + -44 = -44 32k = -44 Divide each side by '32'. k = -1.375 Simplifying k = -1.375
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