Simplify (-3z+6)/(6z^2+14z-80)

$\frac{- 3 z + 6}{6 z^{2} + 14 z - 80}$

Factor $3$ out of $- 3 z + 6$ .

Factor $3$ out of $- 3 z$ .

$\frac{3 (- z) + 6}{6 z^{2} + 14 z - 80}$

Factor $3$ out of $6$ .

$\frac{3 (- z) + 3 (2)}{6 z^{2} + 14 z - 80}$

Factor $3$ out of $3 (- z) + 3 (2)$ .

$\frac{3 (- z + 2)}{6 z^{2} + 14 z - 80}$

Simplify the denominator.

Factor $2$ out of $6 z^{2} + 14 z - 80$ .

Factor $2$ out of $6 z^{2}$ .

$\frac{3 (- z + 2)}{2 (3 z^{2}) + 14 z - 80}$

Factor $2$ out of $14 z$ .

$\frac{3 (- z + 2)}{2 (3 z^{2}) + 2 (7 z) - 80}$

Factor $2$ out of $- 80$ .

$\frac{3 (- z + 2)}{2 (3 z^{2}) + 2 (7 z) + 2 (- 40)}$

Factor $2$ out of $2 (3 z^{2}) + 2 (7 z)$ .

$\frac{3 (- z + 2)}{2 (3 z^{2} + 7 z) + 2 (- 40)}$

Factor $2$ out of $2 (3 z^{2} + 7 z) + 2 (- 40)$ .

$\frac{3 (- z + 2)}{2 (3 z^{2} + 7 z - 40)}$

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 $a \cdot c = 3 \cdot - 40 = - 120$ and whose sum is $b = 7$ .

Factor $7$ out of $7 z$ .

$\frac{3 (- z + 2)}{2 (3 z^{2} + 7 (z) - 40)}$

Rewrite $7$ as $- 8$ plus $15$

$\frac{3 (- z + 2)}{2 (3 z^{2} + (- 8 + 15) z - 40)}$

Apply the distributive property.

$\frac{3 (- z + 2)}{2 (3 z^{2} - 8 z + 15 z - 40)}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{3 (- z + 2)}{2 ((3 z^{2} - 8 z) + 15 z - 40)}$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 z - 8$ .

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

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

Simplify with factoring out.

Factor $- 1$ out of $- z$ .

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

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

$\frac{3 (- (z) - 1 (- 2))}{2 (3 z - 8) (z + 5)}$

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

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

Simplify the expression.

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

$\frac{3 (- 1 (z - 2))}{2 (3 z - 8) (z + 5)}$

Move the negative in front of the fraction.

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

Simplify (-3z+6)/(6z^2+14z-80)

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