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Simplifying 4(5m + -1n) + 5(n + -1m + 3) = 0 (5m * 4 + -1n * 4) + 5(n + -1m + 3) = 0 (20m + -4n) + 5(n + -1m + 3) = 0 Reorder the terms: 20m + -4n + 5(3 + -1m + n) = 0 20m + -4n + (3 * 5 + -1m * 5 + n * 5) = 0 20m + -4n + (15 + -5m + 5n) = 0 Reorder the terms: 15 + 20m + -5m + -4n + 5n = 0 Combine like terms: 20m + -5m = 15m 15 + 15m + -4n + 5n = 0 Combine like terms: -4n + 5n = 1n 15 + 15m + 1n = 0 Solving 15 + 15m + 1n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + 15m + -15 + 1n = 0 + -15 Reorder the terms: 15 + -15 + 15m + 1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 15m + 1n = 0 + -15 15m + 1n = 0 + -15 Combine like terms: 0 + -15 = -15 15m + 1n = -15 Add '-1n' to each side of the equation. 15m + 1n + -1n = -15 + -1n Combine like terms: 1n + -1n = 0 15m + 0 = -15 + -1n 15m = -15 + -1n Divide each side by '15'. m = -1 + -0.06666666667n Simplifying m = -1 + -0.06666666667n
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