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Simplifying 3x(y + z) + -1y(z + x) + 2z(x + y) = 0 (y * 3x + z * 3x) + -1y(z + x) + 2z(x + y) = 0 (3xy + 3xz) + -1y(z + x) + 2z(x + y) = 0 Reorder the terms: 3xy + 3xz + -1y(x + z) + 2z(x + y) = 0 3xy + 3xz + (x * -1y + z * -1y) + 2z(x + y) = 0 3xy + 3xz + (-1xy + -1yz) + 2z(x + y) = 0 3xy + 3xz + -1xy + -1yz + (x * 2z + y * 2z) = 0 3xy + 3xz + -1xy + -1yz + (2xz + 2yz) = 0 Reorder the terms: 3xy + -1xy + 3xz + 2xz + -1yz + 2yz = 0 Combine like terms: 3xy + -1xy = 2xy 2xy + 3xz + 2xz + -1yz + 2yz = 0 Combine like terms: 3xz + 2xz = 5xz 2xy + 5xz + -1yz + 2yz = 0 Combine like terms: -1yz + 2yz = 1yz 2xy + 5xz + 1yz = 0 Solving 2xy + 5xz + 1yz = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1yz' to each side of the equation. 2xy + 5xz + 1yz + -1yz = 0 + -1yz Combine like terms: 1yz + -1yz = 0 2xy + 5xz + 0 = 0 + -1yz 2xy + 5xz = 0 + -1yz Remove the zero: 2xy + 5xz = -1yz Combine like terms: -1yz + yz = 0 2xy + 5xz + yz = 0 The solution to this equation could not be determined.
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