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Simplifying 7(3n + 7(n + k) + 2k) = 0 Reorder the terms: 7(3n + 7(k + n) + 2k) = 0 7(3n + (k * 7 + n * 7) + 2k) = 0 7(3n + (7k + 7n) + 2k) = 0 Reorder the terms: 7(7k + 2k + 3n + 7n) = 0 Combine like terms: 7k + 2k = 9k 7(9k + 3n + 7n) = 0 Combine like terms: 3n + 7n = 10n 7(9k + 10n) = 0 (9k * 7 + 10n * 7) = 0 (63k + 70n) = 0 Solving 63k + 70n = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-70n' to each side of the equation. 63k + 70n + -70n = 0 + -70n Combine like terms: 70n + -70n = 0 63k + 0 = 0 + -70n 63k = 0 + -70n Remove the zero: 63k = -70n Divide each side by '63'. k = -1.111111111n Simplifying k = -1.111111111n
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