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Simplifying (A + -1X)(B + -1X)(C + -1X) = 0 Multiply (A + -1X) * (B + -1X) (A(B + -1X) + -1X * (B + -1X))(C + -1X) = 0 ((B * A + -1X * A) + -1X * (B + -1X))(C + -1X) = 0 ((AB + -1AX) + -1X * (B + -1X))(C + -1X) = 0 (AB + -1AX + (B * -1X + -1X * -1X))(C + -1X) = 0 (AB + -1AX + (-1BX + 1X2))(C + -1X) = 0 (AB + -1AX + -1BX + 1X2)(C + -1X) = 0 Multiply (AB + -1AX + -1BX + 1X2) * (C + -1X) (AB(C + -1X) + -1AX * (C + -1X) + -1BX * (C + -1X) + 1X2 * (C + -1X)) = 0 ((C * AB + -1X * AB) + -1AX * (C + -1X) + -1BX * (C + -1X) + 1X2 * (C + -1X)) = 0 ((ABC + -1ABX) + -1AX * (C + -1X) + -1BX * (C + -1X) + 1X2 * (C + -1X)) = 0 (ABC + -1ABX + (C * -1AX + -1X * -1AX) + -1BX * (C + -1X) + 1X2 * (C + -1X)) = 0 (ABC + -1ABX + (-1ACX + 1AX2) + -1BX * (C + -1X) + 1X2 * (C + -1X)) = 0 (ABC + -1ABX + -1ACX + 1AX2 + (C * -1BX + -1X * -1BX) + 1X2 * (C + -1X)) = 0 (ABC + -1ABX + -1ACX + 1AX2 + (-1BCX + 1BX2) + 1X2 * (C + -1X)) = 0 (ABC + -1ABX + -1ACX + 1AX2 + -1BCX + 1BX2 + (C * 1X2 + -1X * 1X2)) = 0 (ABC + -1ABX + -1ACX + 1AX2 + -1BCX + 1BX2 + (1CX2 + -1X3)) = 0 (ABC + -1ABX + -1ACX + 1AX2 + -1BCX + 1BX2 + 1CX2 + -1X3) = 0 Solving ABC + -1ABX + -1ACX + 1AX2 + -1BCX + 1BX2 + 1CX2 + -1X3 = 0 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add 'BCX' to each side of the equation. ABC + -1ABX + -1ACX + 1AX2 + -1BCX + 1BX2 + 1CX2 + BCX + -1X3 = 0 + BCX Reorder the terms: ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BCX + 1BX2 + 1CX2 + -1X3 = 0 + BCX Combine like terms: -1BCX + BCX = 0 ABC + -1ABX + -1ACX + 1AX2 + 0 + 1BX2 + 1CX2 + -1X3 = 0 + BCX ABC + -1ABX + -1ACX + 1AX2 + 1BX2 + 1CX2 + -1X3 = 0 + BCX Remove the zero: ABC + -1ABX + -1ACX + 1AX2 + 1BX2 + 1CX2 + -1X3 = BCX Add '-1BX2' to each side of the equation. ABC + -1ABX + -1ACX + 1AX2 + 1BX2 + 1CX2 + -1BX2 + -1X3 = BCX + -1BX2 Reorder the terms: ABC + -1ABX + -1ACX + 1AX2 + 1BX2 + -1BX2 + 1CX2 + -1X3 = BCX + -1BX2 Combine like terms: 1BX2 + -1BX2 = 0 ABC + -1ABX + -1ACX + 1AX2 + 0 + 1CX2 + -1X3 = BCX + -1BX2 ABC + -1ABX + -1ACX + 1AX2 + 1CX2 + -1X3 = BCX + -1BX2 Add '-1CX2' to each side of the equation. ABC + -1ABX + -1ACX + 1AX2 + 1CX2 + -1CX2 + -1X3 = BCX + -1BX2 + -1CX2 Combine like terms: 1CX2 + -1CX2 = 0 ABC + -1ABX + -1ACX + 1AX2 + 0 + -1X3 = BCX + -1BX2 + -1CX2 ABC + -1ABX + -1ACX + 1AX2 + -1X3 = BCX + -1BX2 + -1CX2 Add 'X3' to each side of the equation. ABC + -1ABX + -1ACX + 1AX2 + -1X3 + X3 = BCX + -1BX2 + -1CX2 + X3 Combine like terms: -1X3 + X3 = 0 ABC + -1ABX + -1ACX + 1AX2 + 0 = BCX + -1BX2 + -1CX2 + X3 ABC + -1ABX + -1ACX + 1AX2 = BCX + -1BX2 + -1CX2 + X3 Reorder the terms: ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = BCX + -1BCX + -1BX2 + BX2 + -1CX2 + CX2 + X3 + -1X3 Combine like terms: BCX + -1BCX = 0 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = 0 + -1BX2 + BX2 + -1CX2 + CX2 + X3 + -1X3 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = -1BX2 + BX2 + -1CX2 + CX2 + X3 + -1X3 Combine like terms: -1BX2 + BX2 = 0 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = 0 + -1CX2 + CX2 + X3 + -1X3 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = -1CX2 + CX2 + X3 + -1X3 Combine like terms: -1CX2 + CX2 = 0 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = 0 + X3 + -1X3 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = X3 + -1X3 Combine like terms: X3 + -1X3 = 0 ABC + -1ABX + -1ACX + 1AX2 + -1BCX + BX2 + CX2 + -1X3 = 0 The solution to this equation could not be determined.
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