x=(x+1)(x+y)

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Solution for x=(x+1)(x+y) equation: 


Simplifying
x = (x + 1)(x + y)

Reorder the terms:
x = (1 + x)(x + y)

Multiply (1 + x) * (x + y)
x = (1(x + y) + x(x + y))
x = ((x * 1 + y * 1) + x(x + y))
x = ((1x + 1y) + x(x + y))
x = (1x + 1y + (x * x + y * x))

Reorder the terms:
x = (1x + 1y + (xy + x2))
x = (1x + 1y + (xy + x2))

Reorder the terms:
x = (1x + xy + x2 + 1y)
x = (1x + xy + x2 + 1y)

Solving
x = 1x + xy + x2 + 1y

Solving for variable 'x'.

Combine like terms: x + -1x = 0
0 + -1xy + -1x2 + -1y = 1x + xy + x2 + 1y + -1x + -1xy + -1x2 + -1y
-1xy + -1x2 + -1y = 1x + xy + x2 + 1y + -1x + -1xy + -1x2 + -1y

Reorder the terms:
-1xy + -1x2 + -1y = 1x + -1x + xy + -1xy + x2 + -1x2 + 1y + -1y

Combine like terms: 1x + -1x = 0
-1xy + -1x2 + -1y = 0 + xy + -1xy + x2 + -1x2 + 1y + -1y
-1xy + -1x2 + -1y = xy + -1xy + x2 + -1x2 + 1y + -1y

Combine like terms: xy + -1xy = 0
-1xy + -1x2 + -1y = 0 + x2 + -1x2 + 1y + -1y
-1xy + -1x2 + -1y = x2 + -1x2 + 1y + -1y

Combine like terms: x2 + -1x2 = 0
-1xy + -1x2 + -1y = 0 + 1y + -1y
-1xy + -1x2 + -1y = 1y + -1y

Combine like terms: 1y + -1y = 0
-1xy + -1x2 + -1y = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(xy + x2 + y) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(xy + x2 + y)' equal to zero and attempt to solve:

Simplifying
xy + x2 + y = 0

Solving
xy + x2 + y = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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