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Simplifying x(2a + b + c) + -2a + -1b + -1c = 0 (2a * x + b * x + c * x) + -2a + -1b + -1c = 0 (2ax + bx + cx) + -2a + -1b + -1c = 0 Reorder the terms: -2a + 2ax + -1b + bx + -1c + cx = 0 Solving -2a + 2ax + -1b + bx + -1c + cx = 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. -2a + 2ax + -1b + bx + -1c + b + cx = 0 + b Reorder the terms: -2a + 2ax + -1b + b + bx + -1c + cx = 0 + b Combine like terms: -1b + b = 0 -2a + 2ax + 0 + bx + -1c + cx = 0 + b -2a + 2ax + bx + -1c + cx = 0 + b Remove the zero: -2a + 2ax + bx + -1c + cx = b Add '-1bx' to each side of the equation. -2a + 2ax + bx + -1c + -1bx + cx = b + -1bx Reorder the terms: -2a + 2ax + bx + -1bx + -1c + cx = b + -1bx Combine like terms: bx + -1bx = 0 -2a + 2ax + 0 + -1c + cx = b + -1bx -2a + 2ax + -1c + cx = b + -1bx Add 'c' to each side of the equation. -2a + 2ax + -1c + c + cx = b + -1bx + c Combine like terms: -1c + c = 0 -2a + 2ax + 0 + cx = b + -1bx + c -2a + 2ax + cx = b + -1bx + c Add '-1cx' to each side of the equation. -2a + 2ax + cx + -1cx = b + -1bx + c + -1cx Combine like terms: cx + -1cx = 0 -2a + 2ax + 0 = b + -1bx + c + -1cx -2a + 2ax = b + -1bx + c + -1cx Reorder the terms: -2a + 2ax + -1b + bx + -1c + cx = b + -1b + -1bx + bx + c + -1c + -1cx + cx Combine like terms: b + -1b = 0 -2a + 2ax + -1b + bx + -1c + cx = 0 + -1bx + bx + c + -1c + -1cx + cx -2a + 2ax + -1b + bx + -1c + cx = -1bx + bx + c + -1c + -1cx + cx Combine like terms: -1bx + bx = 0 -2a + 2ax + -1b + bx + -1c + cx = 0 + c + -1c + -1cx + cx -2a + 2ax + -1b + bx + -1c + cx = c + -1c + -1cx + cx Combine like terms: c + -1c = 0 -2a + 2ax + -1b + bx + -1c + cx = 0 + -1cx + cx -2a + 2ax + -1b + bx + -1c + cx = -1cx + cx Combine like terms: -1cx + cx = 0 -2a + 2ax + -1b + bx + -1c + cx = 0 The solution to this equation could not be determined.
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