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Simplifying a(m + n) + b(m + n) + -1c(m + n) = 0 (m * a + n * a) + b(m + n) + -1c(m + n) = 0 (am + an) + b(m + n) + -1c(m + n) = 0 am + an + (m * b + n * b) + -1c(m + n) = 0 am + an + (bm + bn) + -1c(m + n) = 0 am + an + bm + bn + (m * -1c + n * -1c) = 0 am + an + bm + bn + (-1cm + -1cn) = 0 Solving am + an + bm + bn + -1cm + -1cn = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bm' to each side of the equation. am + an + bm + bn + -1cm + -1bm + -1cn = 0 + -1bm Reorder the terms: am + an + bm + -1bm + bn + -1cm + -1cn = 0 + -1bm Combine like terms: bm + -1bm = 0 am + an + 0 + bn + -1cm + -1cn = 0 + -1bm am + an + bn + -1cm + -1cn = 0 + -1bm Remove the zero: am + an + bn + -1cm + -1cn = -1bm Add '-1bn' to each side of the equation. am + an + bn + -1cm + -1bn + -1cn = -1bm + -1bn Reorder the terms: am + an + bn + -1bn + -1cm + -1cn = -1bm + -1bn Combine like terms: bn + -1bn = 0 am + an + 0 + -1cm + -1cn = -1bm + -1bn am + an + -1cm + -1cn = -1bm + -1bn Add 'cm' to each side of the equation. am + an + -1cm + cm + -1cn = -1bm + -1bn + cm Combine like terms: -1cm + cm = 0 am + an + 0 + -1cn = -1bm + -1bn + cm am + an + -1cn = -1bm + -1bn + cm Add 'cn' to each side of the equation. am + an + -1cn + cn = -1bm + -1bn + cm + cn Combine like terms: -1cn + cn = 0 am + an + 0 = -1bm + -1bn + cm + cn am + an = -1bm + -1bn + cm + cn Reorder the terms: am + an + bm + bn + -1cm + -1cn = -1bm + bm + -1bn + bn + cm + -1cm + cn + -1cn Combine like terms: -1bm + bm = 0 am + an + bm + bn + -1cm + -1cn = 0 + -1bn + bn + cm + -1cm + cn + -1cn am + an + bm + bn + -1cm + -1cn = -1bn + bn + cm + -1cm + cn + -1cn Combine like terms: -1bn + bn = 0 am + an + bm + bn + -1cm + -1cn = 0 + cm + -1cm + cn + -1cn am + an + bm + bn + -1cm + -1cn = cm + -1cm + cn + -1cn Combine like terms: cm + -1cm = 0 am + an + bm + bn + -1cm + -1cn = 0 + cn + -1cn am + an + bm + bn + -1cm + -1cn = cn + -1cn Combine like terms: cn + -1cn = 0 am + an + bm + bn + -1cm + -1cn = 0 The solution to this equation could not be determined.
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