Factor 2kx+4mx-2nx-3ky-6my+3ny

$2 k x + 4 m x - 2 n x - 3 k y - 6 m y + 3 n y$

Regroup terms.

$2 k x - 3 k y + 4 m x - 2 n x - 6 m y + 3 n y$

Factor $k$ out of $2 k x - 3 k y$ .

Factor $k$ out of $2 k x$ .

$k (2 x) - 3 k y + 4 m x - 2 n x - 6 m y + 3 n y$

Factor $k$ out of $- 3 k y$ .

$k (2 x) + k (- 3 y) + 4 m x - 2 n x - 6 m y + 3 n y$

Factor $k$ out of $k (2 x) + k (- 3 y)$ .

$k (2 x - 3 y) + 4 m x - 2 n x - 6 m y + 3 n y$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$k (2 x - 3 y) + (4 m x - 2 n x) - 6 m y + 3 n y$

Factor out the greatest common factor (GCF) from each group.

$k (2 x - 3 y) + 2 x (2 m - n) - 3 y (2 m - n)$

Factor the polynomial by factoring out the greatest common factor, $2 m - n$ .

$k (2 x - 3 y) + (2 m - n) (2 x - 3 y)$

Factor $2 x - 3 y$ out of $k (2 x - 3 y) + (2 m - n) (2 x - 3 y)$ .

Factor $2 x - 3 y$ out of $k (2 x - 3 y)$ .

$(2 x - 3 y) k + (2 m - n) (2 x - 3 y)$

Factor $2 x - 3 y$ out of $(2 m - n) (2 x - 3 y)$ .

$(2 x - 3 y) k + (2 x - 3 y) (2 m - n)$

Factor $2 x - 3 y$ out of $(2 x - 3 y) k + (2 x - 3 y) (2 m - n)$ .

$(2 x - 3 y) (k + 2 m - n)$