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Simplifying (x + y + -1z)(x + -1y + z) = 0 Multiply (x + y + -1z) * (x + -1y + z) (x(x + -1y + z) + y(x + -1y + z) + -1z * (x + -1y + z)) = 0 ((x * x + -1y * x + z * x) + y(x + -1y + z) + -1z * (x + -1y + z)) = 0 Reorder the terms: ((-1xy + xz + x2) + y(x + -1y + z) + -1z * (x + -1y + z)) = 0 ((-1xy + xz + x2) + y(x + -1y + z) + -1z * (x + -1y + z)) = 0 (-1xy + xz + x2 + (x * y + -1y * y + z * y) + -1z * (x + -1y + z)) = 0 Reorder the terms: (-1xy + xz + x2 + (xy + yz + -1y2) + -1z * (x + -1y + z)) = 0 (-1xy + xz + x2 + (xy + yz + -1y2) + -1z * (x + -1y + z)) = 0 (-1xy + xz + x2 + xy + yz + -1y2 + (x * -1z + -1y * -1z + z * -1z)) = 0 (-1xy + xz + x2 + xy + yz + -1y2 + (-1xz + 1yz + -1z2)) = 0 Reorder the terms: (-1xy + xy + xz + -1xz + x2 + yz + 1yz + -1y2 + -1z2) = 0 Combine like terms: -1xy + xy = 0 (0 + xz + -1xz + x2 + yz + 1yz + -1y2 + -1z2) = 0 (xz + -1xz + x2 + yz + 1yz + -1y2 + -1z2) = 0 Combine like terms: xz + -1xz = 0 (0 + x2 + yz + 1yz + -1y2 + -1z2) = 0 (x2 + yz + 1yz + -1y2 + -1z2) = 0 Combine like terms: yz + 1yz = 2yz (x2 + 2yz + -1y2 + -1z2) = 0 Solving x2 + 2yz + -1y2 + -1z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2yz' to each side of the equation. x2 + 2yz + -1y2 + -2yz + -1z2 = 0 + -2yz Reorder the terms: x2 + 2yz + -2yz + -1y2 + -1z2 = 0 + -2yz Combine like terms: 2yz + -2yz = 0 x2 + 0 + -1y2 + -1z2 = 0 + -2yz x2 + -1y2 + -1z2 = 0 + -2yz Remove the zero: x2 + -1y2 + -1z2 = -2yz Add 'y2' to each side of the equation. x2 + -1y2 + y2 + -1z2 = -2yz + y2 Combine like terms: -1y2 + y2 = 0 x2 + 0 + -1z2 = -2yz + y2 x2 + -1z2 = -2yz + y2 Add 'z2' to each side of the equation. x2 + -1z2 + z2 = -2yz + y2 + z2 Combine like terms: -1z2 + z2 = 0 x2 + 0 = -2yz + y2 + z2 x2 = -2yz + y2 + z2 Simplifying x2 = -2yz + y2 + z2 Reorder the terms: x2 + 2yz + -1y2 + -1z2 = -2yz + 2yz + y2 + -1y2 + z2 + -1z2 Combine like terms: -2yz + 2yz = 0 x2 + 2yz + -1y2 + -1z2 = 0 + y2 + -1y2 + z2 + -1z2 x2 + 2yz + -1y2 + -1z2 = y2 + -1y2 + z2 + -1z2 Combine like terms: y2 + -1y2 = 0 x2 + 2yz + -1y2 + -1z2 = 0 + z2 + -1z2 x2 + 2yz + -1y2 + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 x2 + 2yz + -1y2 + -1z2 = 0 The solution to this equation could not be determined.
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