Factor (6w-11w^2)-(4+7w^2)

$(6 w - 11 w^{2}) - (4 + 7 w^{2})$

Step 1

Remove parentheses.

$6 w - 11 w^{2} - (4 + 7 w^{2})$

Step 2

Factor $- 1$ out of $6 w - 11 w^{2} - (4 + 7 w^{2})$ .

Reorder the expression.

Reorder $4$ and $7 w^{2}$ .

$6 w - 11 w^{2} - (7 w^{2} + 4)$

Move $6 w$ .

$- 11 w^{2} - (7 w^{2} + 4) + 6 w$

Factor $- 1$ out of $- 11 w^{2}$ .

$- (11 w^{2}) - (7 w^{2} + 4) + 6 w$

Factor $- 1$ out of $6 w$ .

$- (11 w^{2}) - (7 w^{2} + 4) - (- 6 w)$

Factor $- 1$ out of $- (11 w^{2}) - (7 w^{2} + 4)$ .

$- (11 w^{2} + 7 w^{2} + 4) - (- 6 w)$

Factor $- 1$ out of $- (11 w^{2} + 7 w^{2} + 4) - (- 6 w)$ .

$- (11 w^{2} + 7 w^{2} + 4 - 6 w)$

Step 3

Add $11 w^{2}$ and $7 w^{2}$ .

$- (18 w^{2} + 4 - 6 w)$

Step 4

Factor $2$ out of $18 w^{2} + 4 - 6 w$ .

Factor $2$ out of $18 w^{2}$ .

$- (2 (9 w^{2}) + 4 - 6 w)$

Factor $2$ out of $4$ .

$- (2 (9 w^{2}) + 2 (2) - 6 w)$

Factor $2$ out of $- 6 w$ .

$- (2 (9 w^{2}) + 2 (2) + 2 (- 3 w))$

Factor $2$ out of $2 (9 w^{2}) + 2 (2)$ .

$- (2 (9 w^{2} + 2) + 2 (- 3 w))$

Factor $2$ out of $2 (9 w^{2} + 2) + 2 (- 3 w)$ .

$- (2 (9 w^{2} + 2 - 3 w))$

Step 5

Factor.

Reorder terms.

$- (2 (9 w^{2} - 3 w + 2))$

Remove unnecessary parentheses.

$- 1 \cdot 2 (9 w^{2} - 3 w + 2)$

Step 6

Multiply $- 1$ by $2$ .

$- 2 (9 w^{2} - 3 w + 2)$