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Simplifying (7 + x)(5 + y)(8 + -1z) = 0 Multiply (7 + x) * (5 + y) (7(5 + y) + x(5 + y))(8 + -1z) = 0 ((5 * 7 + y * 7) + x(5 + y))(8 + -1z) = 0 ((35 + 7y) + x(5 + y))(8 + -1z) = 0 (35 + 7y + (5 * x + y * x))(8 + -1z) = 0 (35 + 7y + (5x + xy))(8 + -1z) = 0 Reorder the terms: (35 + 5x + xy + 7y)(8 + -1z) = 0 (35 + 5x + xy + 7y)(8 + -1z) = 0 Multiply (35 + 5x + xy + 7y) * (8 + -1z) (35(8 + -1z) + 5x * (8 + -1z) + xy(8 + -1z) + 7y * (8 + -1z)) = 0 ((8 * 35 + -1z * 35) + 5x * (8 + -1z) + xy(8 + -1z) + 7y * (8 + -1z)) = 0 ((280 + -35z) + 5x * (8 + -1z) + xy(8 + -1z) + 7y * (8 + -1z)) = 0 (280 + -35z + (8 * 5x + -1z * 5x) + xy(8 + -1z) + 7y * (8 + -1z)) = 0 (280 + -35z + (40x + -5xz) + xy(8 + -1z) + 7y * (8 + -1z)) = 0 (280 + -35z + 40x + -5xz + (8 * xy + -1z * xy) + 7y * (8 + -1z)) = 0 (280 + -35z + 40x + -5xz + (8xy + -1xyz) + 7y * (8 + -1z)) = 0 (280 + -35z + 40x + -5xz + 8xy + -1xyz + (8 * 7y + -1z * 7y)) = 0 (280 + -35z + 40x + -5xz + 8xy + -1xyz + (56y + -7yz)) = 0 Reorder the terms: (280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z) = 0 (280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z) = 0 Solving 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-280' to each side of the equation. 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -280 + -35z = 0 + -280 Reorder the terms: 280 + -280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + -280 Combine like terms: 280 + -280 = 0 0 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + -280 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + -280 Combine like terms: 0 + -280 = -280 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = -280 Add '-56y' to each side of the equation. 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -56y + -35z = -280 + -56y Reorder the terms: 40x + 8xy + -1xyz + -5xz + 56y + -56y + -7yz + -35z = -280 + -56y Combine like terms: 56y + -56y = 0 40x + 8xy + -1xyz + -5xz + 0 + -7yz + -35z = -280 + -56y 40x + 8xy + -1xyz + -5xz + -7yz + -35z = -280 + -56y Add '7yz' to each side of the equation. 40x + 8xy + -1xyz + -5xz + -7yz + 7yz + -35z = -280 + -56y + 7yz Combine like terms: -7yz + 7yz = 0 40x + 8xy + -1xyz + -5xz + 0 + -35z = -280 + -56y + 7yz 40x + 8xy + -1xyz + -5xz + -35z = -280 + -56y + 7yz Add '35z' to each side of the equation. 40x + 8xy + -1xyz + -5xz + -35z + 35z = -280 + -56y + 7yz + 35z Combine like terms: -35z + 35z = 0 40x + 8xy + -1xyz + -5xz + 0 = -280 + -56y + 7yz + 35z 40x + 8xy + -1xyz + -5xz = -280 + -56y + 7yz + 35z Reorder the terms: 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = -280 + -56y + 7yz + 35z + 280 + 56y + -7yz + -35z Reorder the terms: 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = -280 + 280 + -56y + 56y + 7yz + -7yz + 35z + -35z Combine like terms: -280 + 280 = 0 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + -56y + 56y + 7yz + -7yz + 35z + -35z 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = -56y + 56y + 7yz + -7yz + 35z + -35z Combine like terms: -56y + 56y = 0 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + 7yz + -7yz + 35z + -35z 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 7yz + -7yz + 35z + -35z Combine like terms: 7yz + -7yz = 0 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 + 35z + -35z 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 35z + -35z Combine like terms: 35z + -35z = 0 280 + 40x + 8xy + -1xyz + -5xz + 56y + -7yz + -35z = 0 The solution to this equation could not be determined.
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