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Simplifying -10(-2 + -1k) + 4(3 + 4k) = 0 (-2 * -10 + -1k * -10) + 4(3 + 4k) = 0 (20 + 10k) + 4(3 + 4k) = 0 20 + 10k + (3 * 4 + 4k * 4) = 0 20 + 10k + (12 + 16k) = 0 Reorder the terms: 20 + 12 + 10k + 16k = 0 Combine like terms: 20 + 12 = 32 32 + 10k + 16k = 0 Combine like terms: 10k + 16k = 26k 32 + 26k = 0 Solving 32 + 26k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + 26k = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 26k = 0 + -32 26k = 0 + -32 Combine like terms: 0 + -32 = -32 26k = -32 Divide each side by '26'. k = -1.230769231 Simplifying k = -1.230769231
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