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Simplifying (3m + -1n)(m + -2n) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 Multiply (3m + -1n) * (m + -2n) (3m * (m + -2n) + -1n * (m + -2n)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 ((m * 3m + -2n * 3m) + -1n * (m + -2n)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 Reorder the terms: ((-6mn + 3m2) + -1n * (m + -2n)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 ((-6mn + 3m2) + -1n * (m + -2n)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 (-6mn + 3m2 + (m * -1n + -2n * -1n)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 (-6mn + 3m2 + (-1mn + 2n2)) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 Reorder the terms: (-6mn + -1mn + 3m2 + 2n2) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 Combine like terms: -6mn + -1mn = -7mn (-7mn + 3m2 + 2n2) + -1(m + 3n)(2m + n) + -1(m + -1n)(m + n) = 0 Multiply (m + 3n) * (2m + n) -7mn + 3m2 + 2n2 + -1(m(2m + n) + 3n * (2m + n)) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + -1((2m * m + n * m) + 3n * (2m + n)) + -1(m + -1n)(m + n) = 0 Reorder the terms: -7mn + 3m2 + 2n2 + -1((mn + 2m2) + 3n * (2m + n)) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + -1((mn + 2m2) + 3n * (2m + n)) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + -1(mn + 2m2 + (2m * 3n + n * 3n)) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + -1(mn + 2m2 + (6mn + 3n2)) + -1(m + -1n)(m + n) = 0 Reorder the terms: -7mn + 3m2 + 2n2 + -1(mn + 6mn + 2m2 + 3n2) + -1(m + -1n)(m + n) = 0 Combine like terms: mn + 6mn = 7mn -7mn + 3m2 + 2n2 + -1(7mn + 2m2 + 3n2) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + (7mn * -1 + 2m2 * -1 + 3n2 * -1) + -1(m + -1n)(m + n) = 0 -7mn + 3m2 + 2n2 + (-7mn + -2m2 + -3n2) + -1(m + -1n)(m + n) = 0 Multiply (m + -1n) * (m + n) -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(m(m + n) + -1n * (m + n)) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1((m * m + n * m) + -1n * (m + n)) = 0 Reorder the terms: -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1((mn + m2) + -1n * (m + n)) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1((mn + m2) + -1n * (m + n)) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(mn + m2 + (m * -1n + n * -1n)) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(mn + m2 + (-1mn + -1n2)) = 0 Reorder the terms: -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(mn + -1mn + m2 + -1n2) = 0 Combine like terms: mn + -1mn = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(0 + m2 + -1n2) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + -1(m2 + -1n2) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + (m2 * -1 + -1n2 * -1) = 0 -7mn + 3m2 + 2n2 + -7mn + -2m2 + -3n2 + (-1m2 + 1n2) = 0 Reorder the terms: -7mn + -7mn + 3m2 + -2m2 + -1m2 + 2n2 + -3n2 + 1n2 = 0 Combine like terms: -7mn + -7mn = -14mn -14mn + 3m2 + -2m2 + -1m2 + 2n2 + -3n2 + 1n2 = 0 Combine like terms: 3m2 + -2m2 = 1m2 -14mn + 1m2 + -1m2 + 2n2 + -3n2 + 1n2 = 0 Combine like terms: 1m2 + -1m2 = 0 -14mn + 0 + 2n2 + -3n2 + 1n2 = 0 -14mn + 2n2 + -3n2 + 1n2 = 0 Combine like terms: 2n2 + -3n2 = -1n2 -14mn + -1n2 + 1n2 = 0 Combine like terms: -1n2 + 1n2 = 0 -14mn + 0 = 0 -14mn = 0 Solving -14mn = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Divide each side by '-14'. mn = 0 Simplifying mn = 0 The solution to this equation could not be determined.
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