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Simplifying 10m + 12n + 5m + 3n + 5 = 0 Reorder the terms: 5 + 10m + 5m + 12n + 3n = 0 Combine like terms: 10m + 5m = 15m 5 + 15m + 12n + 3n = 0 Combine like terms: 12n + 3n = 15n 5 + 15m + 15n = 0 Solving 5 + 15m + 15n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 15m + -5 + 15n = 0 + -5 Reorder the terms: 5 + -5 + 15m + 15n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 15m + 15n = 0 + -5 15m + 15n = 0 + -5 Combine like terms: 0 + -5 = -5 15m + 15n = -5 Add '-15n' to each side of the equation. 15m + 15n + -15n = -5 + -15n Combine like terms: 15n + -15n = 0 15m + 0 = -5 + -15n 15m = -5 + -15n Divide each side by '15'. m = -0.3333333333 + -1n Simplifying m = -0.3333333333 + -1n
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