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Simplifying (-4 + x)(1 + y)(-6 + -1z) = 0 Multiply (-4 + x) * (1 + y) (-4(1 + y) + x(1 + y))(-6 + -1z) = 0 ((1 * -4 + y * -4) + x(1 + y))(-6 + -1z) = 0 ((-4 + -4y) + x(1 + y))(-6 + -1z) = 0 (-4 + -4y + (1 * x + y * x))(-6 + -1z) = 0 (-4 + -4y + (1x + xy))(-6 + -1z) = 0 Reorder the terms: (-4 + 1x + xy + -4y)(-6 + -1z) = 0 (-4 + 1x + xy + -4y)(-6 + -1z) = 0 Multiply (-4 + 1x + xy + -4y) * (-6 + -1z) (-4(-6 + -1z) + 1x * (-6 + -1z) + xy(-6 + -1z) + -4y * (-6 + -1z)) = 0 ((-6 * -4 + -1z * -4) + 1x * (-6 + -1z) + xy(-6 + -1z) + -4y * (-6 + -1z)) = 0 ((24 + 4z) + 1x * (-6 + -1z) + xy(-6 + -1z) + -4y * (-6 + -1z)) = 0 (24 + 4z + (-6 * 1x + -1z * 1x) + xy(-6 + -1z) + -4y * (-6 + -1z)) = 0 (24 + 4z + (-6x + -1xz) + xy(-6 + -1z) + -4y * (-6 + -1z)) = 0 (24 + 4z + -6x + -1xz + (-6 * xy + -1z * xy) + -4y * (-6 + -1z)) = 0 (24 + 4z + -6x + -1xz + (-6xy + -1xyz) + -4y * (-6 + -1z)) = 0 (24 + 4z + -6x + -1xz + -6xy + -1xyz + (-6 * -4y + -1z * -4y)) = 0 (24 + 4z + -6x + -1xz + -6xy + -1xyz + (24y + 4yz)) = 0 Reorder the terms: (24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z) = 0 (24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z) = 0 Solving 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + -24 + 4z = 0 + -24 Reorder the terms: 24 + -24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -24 -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -24 Combine like terms: 0 + -24 = -24 -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -24 Add '-24y' to each side of the equation. -6x + -6xy + -1xyz + -1xz + 24y + 4yz + -24y + 4z = -24 + -24y Reorder the terms: -6x + -6xy + -1xyz + -1xz + 24y + -24y + 4yz + 4z = -24 + -24y Combine like terms: 24y + -24y = 0 -6x + -6xy + -1xyz + -1xz + 0 + 4yz + 4z = -24 + -24y -6x + -6xy + -1xyz + -1xz + 4yz + 4z = -24 + -24y Add '-4yz' to each side of the equation. -6x + -6xy + -1xyz + -1xz + 4yz + -4yz + 4z = -24 + -24y + -4yz Combine like terms: 4yz + -4yz = 0 -6x + -6xy + -1xyz + -1xz + 0 + 4z = -24 + -24y + -4yz -6x + -6xy + -1xyz + -1xz + 4z = -24 + -24y + -4yz Add '-4z' to each side of the equation. -6x + -6xy + -1xyz + -1xz + 4z + -4z = -24 + -24y + -4yz + -4z Combine like terms: 4z + -4z = 0 -6x + -6xy + -1xyz + -1xz + 0 = -24 + -24y + -4yz + -4z -6x + -6xy + -1xyz + -1xz = -24 + -24y + -4yz + -4z Reorder the terms: 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -24 + -24y + -4yz + -4z + 24 + 24y + 4yz + 4z Reorder the terms: 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -24 + 24 + -24y + 24y + -4yz + 4yz + -4z + 4z Combine like terms: -24 + 24 = 0 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -24y + 24y + -4yz + 4yz + -4z + 4z 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -24y + 24y + -4yz + 4yz + -4z + 4z Combine like terms: -24y + 24y = 0 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -4yz + 4yz + -4z + 4z 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -4yz + 4yz + -4z + 4z Combine like terms: -4yz + 4yz = 0 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 + -4z + 4z 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = -4z + 4z Combine like terms: -4z + 4z = 0 24 + -6x + -6xy + -1xyz + -1xz + 24y + 4yz + 4z = 0 The solution to this equation could not be determined.
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