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This is a quadratic equation in terms of x, y, and z. To solve for x, y, and z, we can rewrite the equation as follows:

x^2 + (4y - 2z)x + (4y^2 - 4yz + z^2) + √(x + y - z) + (x + 1) = 0

Now, we can use the quadratic formula to solve for x in terms of y and z:

x = [-b ± √(b^2 - 4ac)] / 2a

where a = 1, b = 4y - 2z, and c = 4y^2 - 4yz + z^2 + √(x + y - z) + (x + 1).

Substitute these values into the formula and solve for x. Repeat the same process for y and z to find their values.