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Simplifying (2x + -3y + 4z)(2x + -3y + 4z) = 0 Multiply (2x + -3y + 4z) * (2x + -3y + 4z) (2x * (2x + -3y + 4z) + -3y * (2x + -3y + 4z) + 4z * (2x + -3y + 4z)) = 0 ((2x * 2x + -3y * 2x + 4z * 2x) + -3y * (2x + -3y + 4z) + 4z * (2x + -3y + 4z)) = 0 Reorder the terms: ((-6xy + 8xz + 4x2) + -3y * (2x + -3y + 4z) + 4z * (2x + -3y + 4z)) = 0 ((-6xy + 8xz + 4x2) + -3y * (2x + -3y + 4z) + 4z * (2x + -3y + 4z)) = 0 (-6xy + 8xz + 4x2 + (2x * -3y + -3y * -3y + 4z * -3y) + 4z * (2x + -3y + 4z)) = 0 Reorder the terms: (-6xy + 8xz + 4x2 + (-6xy + -12yz + 9y2) + 4z * (2x + -3y + 4z)) = 0 (-6xy + 8xz + 4x2 + (-6xy + -12yz + 9y2) + 4z * (2x + -3y + 4z)) = 0 (-6xy + 8xz + 4x2 + -6xy + -12yz + 9y2 + (2x * 4z + -3y * 4z + 4z * 4z)) = 0 (-6xy + 8xz + 4x2 + -6xy + -12yz + 9y2 + (8xz + -12yz + 16z2)) = 0 Reorder the terms: (-6xy + -6xy + 8xz + 8xz + 4x2 + -12yz + -12yz + 9y2 + 16z2) = 0 Combine like terms: -6xy + -6xy = -12xy (-12xy + 8xz + 8xz + 4x2 + -12yz + -12yz + 9y2 + 16z2) = 0 Combine like terms: 8xz + 8xz = 16xz (-12xy + 16xz + 4x2 + -12yz + -12yz + 9y2 + 16z2) = 0 Combine like terms: -12yz + -12yz = -24yz (-12xy + 16xz + 4x2 + -24yz + 9y2 + 16z2) = 0 Solving -12xy + 16xz + 4x2 + -24yz + 9y2 + 16z2 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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