2x=x+7xy

Solution for 2x=x+7xy equation:

Simplifying
2x = x + 7xy

Solving
2x = x + 7xy

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
2x + -1x = x + -1x + 7xy

Combine like terms: 2x + -1x = 1x
1x = x + -1x + 7xy

Combine like terms: x + -1x = 0
1x = 0 + 7xy
1x = 7xy

Add '-7xy' to each side of the equation.
1x + -7xy = 7xy + -7xy

Combine like terms: 7xy + -7xy = 0
1x + -7xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -7y) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + -7y)' equal to zero and attempt to solve:

Simplifying
1 + -7y = 0

Solving
1 + -7y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7y = 0 + -1
-7y = 0 + -1

Combine like terms: 0 + -1 = -1
-7y = -1

Add '7y' to each side of the equation.
-7y + 7y = -1 + 7y

Combine like terms: -7y + 7y = 0
0 = -1 + 7y

Simplifying
0 = -1 + 7y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}