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Simplifying (x + -1y)(x + -1z)(x + -1t) = 0 Reorder the terms: (x + -1y)(x + -1z)(-1t + x) = 0 Multiply (x + -1y) * (x + -1z) (x(x + -1z) + -1y * (x + -1z))(-1t + x) = 0 ((x * x + -1z * x) + -1y * (x + -1z))(-1t + x) = 0 Reorder the terms: ((-1xz + x2) + -1y * (x + -1z))(-1t + x) = 0 ((-1xz + x2) + -1y * (x + -1z))(-1t + x) = 0 (-1xz + x2 + (x * -1y + -1z * -1y))(-1t + x) = 0 (-1xz + x2 + (-1xy + 1yz))(-1t + x) = 0 Reorder the terms: (-1xy + -1xz + x2 + 1yz)(-1t + x) = 0 (-1xy + -1xz + x2 + 1yz)(-1t + x) = 0 Multiply (-1xy + -1xz + x2 + 1yz) * (-1t + x) (-1xy * (-1t + x) + -1xz * (-1t + x) + x2(-1t + x) + 1yz * (-1t + x)) = 0 ((-1t * -1xy + x * -1xy) + -1xz * (-1t + x) + x2(-1t + x) + 1yz * (-1t + x)) = 0 ((1txy + -1x2y) + -1xz * (-1t + x) + x2(-1t + x) + 1yz * (-1t + x)) = 0 (1txy + -1x2y + (-1t * -1xz + x * -1xz) + x2(-1t + x) + 1yz * (-1t + x)) = 0 (1txy + -1x2y + (1txz + -1x2z) + x2(-1t + x) + 1yz * (-1t + x)) = 0 (1txy + -1x2y + 1txz + -1x2z + (-1t * x2 + x * x2) + 1yz * (-1t + x)) = 0 (1txy + -1x2y + 1txz + -1x2z + (-1tx2 + x3) + 1yz * (-1t + x)) = 0 (1txy + -1x2y + 1txz + -1x2z + -1tx2 + x3 + (-1t * 1yz + x * 1yz)) = 0 (1txy + -1x2y + 1txz + -1x2z + -1tx2 + x3 + (-1tyz + 1xyz)) = 0 Reorder the terms: (1txy + 1txz + -1tx2 + -1tyz + 1xyz + -1x2y + -1x2z + x3) = 0 (1txy + 1txz + -1tx2 + -1tyz + 1xyz + -1x2y + -1x2z + x3) = 0 Solving 1txy + 1txz + -1tx2 + -1tyz + 1xyz + -1x2y + -1x2z + x3 = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1xyz' to each side of the equation. 1txy + 1txz + -1tx2 + -1tyz + 1xyz + -1x2y + -1x2z + -1xyz + x3 = 0 + -1xyz Reorder the terms: 1txy + 1txz + -1tx2 + -1tyz + 1xyz + -1xyz + -1x2y + -1x2z + x3 = 0 + -1xyz Combine like terms: 1xyz + -1xyz = 0 1txy + 1txz + -1tx2 + -1tyz + 0 + -1x2y + -1x2z + x3 = 0 + -1xyz 1txy + 1txz + -1tx2 + -1tyz + -1x2y + -1x2z + x3 = 0 + -1xyz Remove the zero: 1txy + 1txz + -1tx2 + -1tyz + -1x2y + -1x2z + x3 = -1xyz Add 'x2y' to each side of the equation. 1txy + 1txz + -1tx2 + -1tyz + -1x2y + -1x2z + x2y + x3 = -1xyz + x2y Reorder the terms: 1txy + 1txz + -1tx2 + -1tyz + -1x2y + x2y + -1x2z + x3 = -1xyz + x2y Combine like terms: -1x2y + x2y = 0 1txy + 1txz + -1tx2 + -1tyz + 0 + -1x2z + x3 = -1xyz + x2y 1txy + 1txz + -1tx2 + -1tyz + -1x2z + x3 = -1xyz + x2y Add 'x2z' to each side of the equation. 1txy + 1txz + -1tx2 + -1tyz + -1x2z + x2z + x3 = -1xyz + x2y + x2z Combine like terms: -1x2z + x2z = 0 1txy + 1txz + -1tx2 + -1tyz + 0 + x3 = -1xyz + x2y + x2z 1txy + 1txz + -1tx2 + -1tyz + x3 = -1xyz + x2y + x2z Add '-1x3' to each side of the equation. 1txy + 1txz + -1tx2 + -1tyz + x3 + -1x3 = -1xyz + x2y + x2z + -1x3 Combine like terms: x3 + -1x3 = 0 1txy + 1txz + -1tx2 + -1tyz + 0 = -1xyz + x2y + x2z + -1x3 1txy + 1txz + -1tx2 + -1tyz = -1xyz + x2y + x2z + -1x3 Reorder the terms: 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = -1xyz + xyz + x2y + -1x2y + x2z + -1x2z + -1x3 + x3 Combine like terms: -1xyz + xyz = 0 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = 0 + x2y + -1x2y + x2z + -1x2z + -1x3 + x3 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = x2y + -1x2y + x2z + -1x2z + -1x3 + x3 Combine like terms: x2y + -1x2y = 0 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = 0 + x2z + -1x2z + -1x3 + x3 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = x2z + -1x2z + -1x3 + x3 Combine like terms: x2z + -1x2z = 0 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = 0 + -1x3 + x3 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 1txy + 1txz + -1tx2 + -1tyz + xyz + -1x2y + -1x2z + x3 = 0 The solution to this equation could not be determined.
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