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Simplifying M(m + n) + n(2m + 3n) = 0 (m * M + n * M) + n(2m + 3n) = 0 (mM + nM) + n(2m + 3n) = 0 mM + nM + (2m * n + 3n * n) = 0 mM + nM + (2mn + 3n2) = 0 Reorder the terms: mM + 2mn + nM + 3n2 = 0 Solving mM + 2mn + nM + 3n2 = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1nM' to each side of the equation. mM + 2mn + nM + -1nM + 3n2 = 0 + -1nM Combine like terms: nM + -1nM = 0 mM + 2mn + 0 + 3n2 = 0 + -1nM mM + 2mn + 3n2 = 0 + -1nM Remove the zero: mM + 2mn + 3n2 = -1nM Add '-3n2' to each side of the equation. mM + 2mn + 3n2 + -3n2 = -1nM + -3n2 Combine like terms: 3n2 + -3n2 = 0 mM + 2mn + 0 = -1nM + -3n2 mM + 2mn = -1nM + -3n2 Reorder the terms: mM + 2mn + nM + 3n2 = -1nM + nM + -3n2 + 3n2 Combine like terms: -1nM + nM = 0 mM + 2mn + nM + 3n2 = 0 + -3n2 + 3n2 mM + 2mn + nM + 3n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 mM + 2mn + nM + 3n2 = 0 The solution to this equation could not be determined.
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