7x^2y-14xy^2+21xy=0

Solution for 7x^2y-14xy^2+21xy=0 equation:

Simplifying
7x2y + -14xy2 + 21xy = 0

Reorder the terms:
21xy + -14xy2 + 7x2y = 0

Solving
21xy + -14xy2 + 7x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7xy'.
7xy(3 + -2y + x) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve:

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -2y + x)' equal to zero and attempt to solve:

Simplifying
3 + -2y + x = 0

Reorder the terms:
3 + x + -2y = 0

Solving
3 + x + -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 + x + -3 + -2y = 0 + -3

Reorder the terms:
3 + -3 + x + -2y = 0 + -3

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

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

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

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

Simplifying
x = -3 + 2y
Solution
x = {-3 + 2y}