Factor 3a(2x-7)+5b(7-2x)

$3 a (2 x - 7) + 5 b (7 - 2 x)$

Apply the distributive property.

$3 a (2 x) + 3 a \cdot - 7 + 5 b (7 - 2 x)$

Rewrite using the commutative property of multiplication.

$3 \cdot 2 a x + 3 a \cdot - 7 + 5 b (7 - 2 x)$

Multiply $- 7$ by $3$ .

$3 \cdot 2 a x - 21 a + 5 b (7 - 2 x)$

Multiply $3$ by $2$ .

$6 a x - 21 a + 5 b (7 - 2 x)$

Apply the distributive property.

$6 a x - 21 a + 5 b \cdot 7 + 5 b (- 2 x)$

Multiply $7$ by $5$ .

$6 a x - 21 a + 35 b + 5 b (- 2 x)$

Rewrite using the commutative property of multiplication.

$6 a x - 21 a + 35 b + 5 \cdot - 2 b x$

Multiply $5$ by $- 2$ .

$6 a x - 21 a + 35 b - 10 b x$

Rewrite $6 a x - 21 a + 35 b - 10 b x$ in a factored form.

Reorder terms.

$- 21 a + 35 b + 6 a x - 10 b x$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 21 a + 35 b) + 6 a x - 10 b x$

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

$7 (- 3 a + 5 b) - 2 x (- 3 a + 5 b)$

Factor the polynomial by factoring out the greatest common factor, $- 3 a + 5 b$ .

$(- 3 a + 5 b) (7 - 2 x)$

Factor $- 1$ out of $- 3 a + 5 b$ .

Factor $- 1$ out of $- 3 a$ .

$(- (3 a) + 5 b) (7 - 2 x)$

Factor $- 1$ out of $5 b$ .

$(- (3 a) - (- 5 b)) (7 - 2 x)$

Factor $- 1$ out of $- (3 a) - (- 5 b)$ .

$- (3 a - 5 b) (7 - 2 x)$