2x+3xy+4x+5xy+6x=0

Solution for 2x+3xy+4x+5xy+6x=0 equation:

Simplifying
2x + 3xy + 4x + 5xy + 6x = 0

Reorder the terms:
2x + 4x + 6x + 3xy + 5xy = 0

Combine like terms: 2x + 4x = 6x
6x + 6x + 3xy + 5xy = 0

Combine like terms: 6x + 6x = 12x
12x + 3xy + 5xy = 0

Combine like terms: 3xy + 5xy = 8xy
12x + 8xy = 0

Solving
12x + 8xy = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + 2y) = 0

Ignore the factor 4.
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 '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Add '-2y' to each side of the equation.
2y + -2y = -3 + -2y

Combine like terms: 2y + -2y = 0
0 = -3 + -2y

Simplifying
0 = -3 + -2y

The solution to this equation could not be determined.

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