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Simplifying (m + -1n)(n + m) = 0 Reorder the terms: (m + -1n)(m + n) = 0 Multiply (m + -1n) * (m + n) (m(m + n) + -1n * (m + n)) = 0 ((m * m + n * m) + -1n * (m + n)) = 0 Reorder the terms: ((mn + m2) + -1n * (m + n)) = 0 ((mn + m2) + -1n * (m + n)) = 0 (mn + m2 + (m * -1n + n * -1n)) = 0 (mn + m2 + (-1mn + -1n2)) = 0 Reorder the terms: (mn + -1mn + m2 + -1n2) = 0 Combine like terms: mn + -1mn = 0 (0 + m2 + -1n2) = 0 (m2 + -1n2) = 0 Solving m2 + -1n2 = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add 'n2' to each side of the equation. m2 + -1n2 + n2 = 0 + n2 Combine like terms: -1n2 + n2 = 0 m2 + 0 = 0 + n2 m2 = 0 + n2 Remove the zero: m2 = n2 Simplifying m2 = n2 Take the square root of each side: m = {-1n, n}
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