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Simplifying 5(8k + -3) + 2(-2k + 9) = 0 Reorder the terms: 5(-3 + 8k) + 2(-2k + 9) = 0 (-3 * 5 + 8k * 5) + 2(-2k + 9) = 0 (-15 + 40k) + 2(-2k + 9) = 0 Reorder the terms: -15 + 40k + 2(9 + -2k) = 0 -15 + 40k + (9 * 2 + -2k * 2) = 0 -15 + 40k + (18 + -4k) = 0 Reorder the terms: -15 + 18 + 40k + -4k = 0 Combine like terms: -15 + 18 = 3 3 + 40k + -4k = 0 Combine like terms: 40k + -4k = 36k 3 + 36k = 0 Solving 3 + 36k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 36k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 36k = 0 + -3 36k = 0 + -3 Combine like terms: 0 + -3 = -3 36k = -3 Divide each side by '36'. k = -0.08333333333 Simplifying k = -0.08333333333
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