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Simplifying 4k + 3mn + -2(5mn + -1k) = 0 Reorder the terms: 4k + 3mn + -2(-1k + 5mn) = 0 4k + 3mn + (-1k * -2 + 5mn * -2) = 0 4k + 3mn + (2k + -10mn) = 0 Reorder the terms: 4k + 2k + 3mn + -10mn = 0 Combine like terms: 4k + 2k = 6k 6k + 3mn + -10mn = 0 Combine like terms: 3mn + -10mn = -7mn 6k + -7mn = 0 Solving 6k + -7mn = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7mn' to each side of the equation. 6k + -7mn + 7mn = 0 + 7mn Combine like terms: -7mn + 7mn = 0 6k + 0 = 0 + 7mn 6k = 0 + 7mn Remove the zero: 6k = 7mn Divide each side by '6'. k = 1.166666667mn Simplifying k = 1.166666667mn
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