Factor 7xy-3n-x+21ny

$7 x y - 3 n - x + 21 n y$

Regroup terms.

$- x + 7 x y - 3 n + 21 n y$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x + 7 x y) - 3 n + 21 n y$

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

$x \cdot (- 1 + 7 y) + 3 n (- 1 + 7 y)$

Factor the polynomial by factoring out the greatest common factor, $- 1 + 7 y$ .

$(- 1 + 7 y) (x + 3 n)$

Factor $- 1$ out of $- 1 + 7 y$ .

Reorder $- 1$ and $7 y$ .

$(7 y - 1) (x + 3 n)$

Factor $- 1$ out of $7 y$ .

$(- (- 7 y) - 1) (x + 3 n)$

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

$(- (- 7 y) - 1 (1)) (x + 3 n)$

Factor $- 1$ out of $- (- 7 y) - 1 (1)$ .

$- (- 7 y + 1) (x + 3 n)$

Factor.

Factor $- 1$ out of $- 7 y + 1$ .

Factor $- 1$ out of $- 7 y$ .

$- (- (7 y) + 1) (x + 3 n)$

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

$- (- (7 y) - 1 (- 1)) (x + 3 n)$

Factor $- 1$ out of $- (7 y) - 1 (- 1)$ .

$- - (7 y - 1) (x + 3 n)$

Remove unnecessary parentheses.

$- - 1 (7 y - 1) (x + 3 n)$

Combine exponents.

Factor out negative.

$- ((- (7 y - 1)) (x + 3 n))$

Multiply $- 1$ by $- 1$ .

$1 ((7 y - 1) (x + 3 n))$

Multiply $7 y - 1$ by $1$ .

$(7 y - 1) (x + 3 n)$