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Simplifying (x + -1a)(x + -1c) + -1b = 0 Reorder the terms: (-1a + x)(x + -1c) + -1b = 0 Reorder the terms: (-1a + x)(-1c + x) + -1b = 0 Multiply (-1a + x) * (-1c + x) (-1a * (-1c + x) + x(-1c + x)) + -1b = 0 ((-1c * -1a + x * -1a) + x(-1c + x)) + -1b = 0 ((1ac + -1ax) + x(-1c + x)) + -1b = 0 (1ac + -1ax + (-1c * x + x * x)) + -1b = 0 (1ac + -1ax + (-1cx + x2)) + -1b = 0 (1ac + -1ax + -1cx + x2) + -1b = 0 Reorder the terms: 1ac + -1ax + -1b + -1cx + x2 = 0 Solving 1ac + -1ax + -1b + -1cx + x2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 1ac + -1ax + -1b + -1cx + b + x2 = 0 + b Reorder the terms: 1ac + -1ax + -1b + b + -1cx + x2 = 0 + b Combine like terms: -1b + b = 0 1ac + -1ax + 0 + -1cx + x2 = 0 + b 1ac + -1ax + -1cx + x2 = 0 + b Remove the zero: 1ac + -1ax + -1cx + x2 = b Add 'cx' to each side of the equation. 1ac + -1ax + -1cx + cx + x2 = b + cx Combine like terms: -1cx + cx = 0 1ac + -1ax + 0 + x2 = b + cx 1ac + -1ax + x2 = b + cx Add '-1x2' to each side of the equation. 1ac + -1ax + x2 + -1x2 = b + cx + -1x2 Combine like terms: x2 + -1x2 = 0 1ac + -1ax + 0 = b + cx + -1x2 1ac + -1ax = b + cx + -1x2 Reorder the terms: 1ac + -1ax + -1b + -1cx + x2 = b + -1b + cx + -1cx + -1x2 + x2 Combine like terms: b + -1b = 0 1ac + -1ax + -1b + -1cx + x2 = 0 + cx + -1cx + -1x2 + x2 1ac + -1ax + -1b + -1cx + x2 = cx + -1cx + -1x2 + x2 Combine like terms: cx + -1cx = 0 1ac + -1ax + -1b + -1cx + x2 = 0 + -1x2 + x2 1ac + -1ax + -1b + -1cx + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1ac + -1ax + -1b + -1cx + x2 = 0 The solution to this equation could not be determined.
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