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Simplifying 4(m + 3n) + -1(m + -2n) = 0 (m * 4 + 3n * 4) + -1(m + -2n) = 0 (4m + 12n) + -1(m + -2n) = 0 4m + 12n + (m * -1 + -2n * -1) = 0 4m + 12n + (-1m + 2n) = 0 Reorder the terms: 4m + -1m + 12n + 2n = 0 Combine like terms: 4m + -1m = 3m 3m + 12n + 2n = 0 Combine like terms: 12n + 2n = 14n 3m + 14n = 0 Solving 3m + 14n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-14n' to each side of the equation. 3m + 14n + -14n = 0 + -14n Combine like terms: 14n + -14n = 0 3m + 0 = 0 + -14n 3m = 0 + -14n Remove the zero: 3m = -14n Divide each side by '3'. m = -4.666666667n Simplifying m = -4.666666667n
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