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Simplifying 4(2 + 4k) + 3(7k + 1) * 8 = 0 (2 * 4 + 4k * 4) + 3(7k + 1) * 8 = 0 (8 + 16k) + 3(7k + 1) * 8 = 0 Reorder the terms: 8 + 16k + 3(1 + 7k) * 8 = 0 Reorder the terms for easier multiplication: 8 + 16k + 3 * 8(1 + 7k) = 0 Multiply 3 * 8 8 + 16k + 24(1 + 7k) = 0 8 + 16k + (1 * 24 + 7k * 24) = 0 8 + 16k + (24 + 168k) = 0 Reorder the terms: 8 + 24 + 16k + 168k = 0 Combine like terms: 8 + 24 = 32 32 + 16k + 168k = 0 Combine like terms: 16k + 168k = 184k 32 + 184k = 0 Solving 32 + 184k = 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 + 184k = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 184k = 0 + -32 184k = 0 + -32 Combine like terms: 0 + -32 = -32 184k = -32 Divide each side by '184'. k = -0.1739130435 Simplifying k = -0.1739130435
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