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Simplifying 4(m + n) + 2(2m + 2n) = 0 (m * 4 + n * 4) + 2(2m + 2n) = 0 (4m + 4n) + 2(2m + 2n) = 0 4m + 4n + (2m * 2 + 2n * 2) = 0 4m + 4n + (4m + 4n) = 0 Reorder the terms: 4m + 4m + 4n + 4n = 0 Combine like terms: 4m + 4m = 8m 8m + 4n + 4n = 0 Combine like terms: 4n + 4n = 8n 8m + 8n = 0 Solving 8m + 8n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8n' to each side of the equation. 8m + 8n + -8n = 0 + -8n Combine like terms: 8n + -8n = 0 8m + 0 = 0 + -8n 8m = 0 + -8n Remove the zero: 8m = -8n Divide each side by '8'. m = -1n Simplifying m = -1n
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