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Simplifying 2(2m + -1n) + 4(m + 2n) + -5(4m + -3n) + -3(m + 4n) = 0 (2m * 2 + -1n * 2) + 4(m + 2n) + -5(4m + -3n) + -3(m + 4n) = 0 (4m + -2n) + 4(m + 2n) + -5(4m + -3n) + -3(m + 4n) = 0 4m + -2n + (m * 4 + 2n * 4) + -5(4m + -3n) + -3(m + 4n) = 0 4m + -2n + (4m + 8n) + -5(4m + -3n) + -3(m + 4n) = 0 4m + -2n + 4m + 8n + (4m * -5 + -3n * -5) + -3(m + 4n) = 0 4m + -2n + 4m + 8n + (-20m + 15n) + -3(m + 4n) = 0 4m + -2n + 4m + 8n + -20m + 15n + (m * -3 + 4n * -3) = 0 4m + -2n + 4m + 8n + -20m + 15n + (-3m + -12n) = 0 Reorder the terms: 4m + 4m + -20m + -3m + -2n + 8n + 15n + -12n = 0 Combine like terms: 4m + 4m = 8m 8m + -20m + -3m + -2n + 8n + 15n + -12n = 0 Combine like terms: 8m + -20m = -12m -12m + -3m + -2n + 8n + 15n + -12n = 0 Combine like terms: -12m + -3m = -15m -15m + -2n + 8n + 15n + -12n = 0 Combine like terms: -2n + 8n = 6n -15m + 6n + 15n + -12n = 0 Combine like terms: 6n + 15n = 21n -15m + 21n + -12n = 0 Combine like terms: 21n + -12n = 9n -15m + 9n = 0 Solving -15m + 9n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9n' to each side of the equation. -15m + 9n + -9n = 0 + -9n Combine like terms: 9n + -9n = 0 -15m + 0 = 0 + -9n -15m = 0 + -9n Remove the zero: -15m = -9n Divide each side by '-15'. m = 0.6n Simplifying m = 0.6n
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