Factor 6m-n-3mn+2

$6 m - n - 3 m n + 2$

Step 1

Reorder terms.

$- 3 m n + 6 m - n + 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 3 m n + 6 m) - n + 2$

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

$3 m (- 1 n + 2) + 1 (- n + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- 1 n + 2$ .

$(- 1 n + 2) (3 m + 1)$

Step 4

Rewrite $- 1 n$ as $- n$ .

$(- n + 2) (3 m + 1)$

Step 5

Factor $- 1$ out of $- n + 2$ .

Factor $- 1$ out of $- n$ .

$(- (n) + 2) (3 m + 1)$

Rewrite $2$ as $- 1 (- 2)$ .

$(- (n) - 1 (- 2)) (3 m + 1)$

Factor $- 1$ out of $- (n) - 1 (- 2)$ .

$- (n - 2) (3 m + 1)$