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Simplifying 5(2m + 3n) + 3(m + -7) = 0 (2m * 5 + 3n * 5) + 3(m + -7) = 0 (10m + 15n) + 3(m + -7) = 0 Reorder the terms: 10m + 15n + 3(-7 + m) = 0 10m + 15n + (-7 * 3 + m * 3) = 0 10m + 15n + (-21 + 3m) = 0 Reorder the terms: -21 + 10m + 3m + 15n = 0 Combine like terms: 10m + 3m = 13m -21 + 13m + 15n = 0 Solving -21 + 13m + 15n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 13m + 21 + 15n = 0 + 21 Reorder the terms: -21 + 21 + 13m + 15n = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 13m + 15n = 0 + 21 13m + 15n = 0 + 21 Combine like terms: 0 + 21 = 21 13m + 15n = 21 Add '-15n' to each side of the equation. 13m + 15n + -15n = 21 + -15n Combine like terms: 15n + -15n = 0 13m + 0 = 21 + -15n 13m = 21 + -15n Divide each side by '13'. m = 1.615384615 + -1.153846154n Simplifying m = 1.615384615 + -1.153846154n
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