Divide ((45x^2-42x-48)/(5x-8))

$(\frac{45 x^{2} - 42 x - 48}{5 x - 8})$

Remove parentheses.

$\frac{45 x^{2} - 42 x - 48}{5 x - 8}$

Simplify the numerator.

Factor $3$ out of $45 x^{2} - 42 x - 48$ .

Factor $3$ out of $45 x^{2}$ .

$\frac{3 (15 x^{2}) - 42 x - 48}{5 x - 8}$

Factor $3$ out of $- 42 x$ .

$\frac{3 (15 x^{2}) + 3 (- 14 x) - 48}{5 x - 8}$

Factor $3$ out of $- 48$ .

$\frac{3 (15 x^{2}) + 3 (- 14 x) + 3 (- 16)}{5 x - 8}$

Factor $3$ out of $3 (15 x^{2}) + 3 (- 14 x)$ .

$\frac{3 (15 x^{2} - 14 x) + 3 (- 16)}{5 x - 8}$

Factor $3$ out of $3 (15 x^{2} - 14 x) + 3 (- 16)$ .

$\frac{3 (15 x^{2} - 14 x - 16)}{5 x - 8}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 15 \cdot - 16 = - 240$ and whose sum is $b = - 14$ .

Factor $- 14$ out of $- 14 x$ .

$\frac{3 (15 x^{2} - 14 (x) - 16)}{5 x - 8}$

Rewrite $- 14$ as $10$ plus $- 24$

$\frac{3 (15 x^{2} + (10 - 24) x - 16)}{5 x - 8}$

Apply the distributive property.

$\frac{3 (15 x^{2} + 10 x - 24 x - 16)}{5 x - 8}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{3 ((15 x^{2} + 10 x) - 24 x - 16)}{5 x - 8}$

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

$\frac{3 (5 x (3 x + 2) - 8 (3 x + 2))}{5 x - 8}$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$\frac{3 ((3 x + 2) (5 x - 8))}{5 x - 8}$

$\frac{3 (3 x + 2) (5 x - 8)}{5 x - 8}$

Cancel the common factor of $5 x - 8$ .

Cancel the common factor.

$\frac{3 (3 x + 2) (5 x - 8)}{5 x - 8}$

Divide $3 (3 x + 2)$ by $1$ .

$3 (3 x + 2)$

Apply the distributive property.

$3 (3 x) + 3 \cdot 2$

Multiply $3$ by $3$ .

$9 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$9 x + 6$

Divide ((45x^2-42x-48)/(5x-8))

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