x^2+2x+2=(x+y)(x+z)

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Solution for x^2+2x+2=(x+y)(x+z) equation: 


Simplifying
x2 + 2x + 2 = (x + y)(x + z)

Reorder the terms:
2 + 2x + x2 = (x + y)(x + z)

Multiply (x + y) * (x + z)
2 + 2x + x2 = (x(x + z) + y(x + z))
2 + 2x + x2 = ((x * x + z * x) + y(x + z))

Reorder the terms:
2 + 2x + x2 = ((xz + x2) + y(x + z))
2 + 2x + x2 = ((xz + x2) + y(x + z))
2 + 2x + x2 = (xz + x2 + (x * y + z * y))
2 + 2x + x2 = (xz + x2 + (xy + yz))

Reorder the terms:
2 + 2x + x2 = (xy + xz + x2 + yz)
2 + 2x + x2 = (xy + xz + x2 + yz)

Add '-1x2' to each side of the equation.
2 + 2x + x2 + -1x2 = xy + xz + x2 + -1x2 + yz

Combine like terms: x2 + -1x2 = 0
2 + 2x + 0 = xy + xz + x2 + -1x2 + yz
2 + 2x = xy + xz + x2 + -1x2 + yz

Combine like terms: x2 + -1x2 = 0
2 + 2x = xy + xz + 0 + yz
2 + 2x = xy + xz + yz

Solving
2 + 2x = xy + xz + yz

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1xy' to each side of the equation.
2 + 2x + -1xy = xy + xz + -1xy + yz

Reorder the terms:
2 + 2x + -1xy = xy + -1xy + xz + yz

Combine like terms: xy + -1xy = 0
2 + 2x + -1xy = 0 + xz + yz
2 + 2x + -1xy = xz + yz

Add '-1xz' to each side of the equation.
2 + 2x + -1xy + -1xz = xz + -1xz + yz

Combine like terms: xz + -1xz = 0
2 + 2x + -1xy + -1xz = 0 + yz
2 + 2x + -1xy + -1xz = yz

Add '-2' to each side of the equation.
2 + 2x + -1xy + -2 + -1xz = -2 + yz

Reorder the terms:
2 + -2 + 2x + -1xy + -1xz = -2 + yz

Combine like terms: 2 + -2 = 0
0 + 2x + -1xy + -1xz = -2 + yz
2x + -1xy + -1xz = -2 + yz

Reorder the terms:
2 + 2x + -1xy + -1xz + -1yz = -2 + yz + 2 + -1yz

Reorder the terms:
2 + 2x + -1xy + -1xz + -1yz = -2 + 2 + yz + -1yz

Combine like terms: -2 + 2 = 0
2 + 2x + -1xy + -1xz + -1yz = 0 + yz + -1yz
2 + 2x + -1xy + -1xz + -1yz = yz + -1yz

Combine like terms: yz + -1yz = 0
2 + 2x + -1xy + -1xz + -1yz = 0

The solution to this equation could not be determined.

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