Basic Math Examples

$3 c + 2 - (9 c^{2} - 3 c - 6)$

Step 1

Apply the distributive property.

$3 c + 2 - (9 c^{2}) - (- 3 c) - - 6$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Multiply $9$ by $- 1$ .

$3 c + 2 - 9 c^{2} - (- 3 c) - - 6$

Step 2.2

Multiply $- 3$ by $- 1$ .

$3 c + 2 - 9 c^{2} + 3 c - - 6$

Step 2.3

Multiply $- 1$ by $- 6$ .

$3 c + 2 - 9 c^{2} + 3 c + 6$

Step 3

Add $3 c$ and $3 c$ .

$6 c + 2 - 9 c^{2} + 6$

Step 4

Add $2$ and $6$ .

$6 c - 9 c^{2} + 8$

Step 5

Reorder terms.

$- 9 c^{2} + 6 c + 8$

Step 6

Rewrite $- 9 c^{2} + 6 c + 8$ in a factored form.

Tap for more steps...

Step 6.1

Factor $- 1$ out of $- 9 c^{2} + 6 c + 8$ .

Tap for more steps...

Step 6.1.1

Factor $- 1$ out of $- 9 c^{2}$ .

$- (9 c^{2}) + 6 c + 8$

Step 6.1.2

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

$- (9 c^{2}) - (- 6 c) + 8$

Step 6.1.3

Rewrite $8$ as $- 1 (- 8)$ .

$- (9 c^{2}) - (- 6 c) - 1 (- 8)$

Step 6.1.4

Factor $- 1$ out of $- (9 c^{2}) - (- 6 c)$ .

$- (9 c^{2} - 6 c) - 1 (- 8)$

Step 6.1.5

Factor $- 1$ out of $- (9 c^{2} - 6 c) - 1 (- 8)$ .

$- (9 c^{2} - 6 c - 8)$

Step 6.2

Factor.

Tap for more steps...

Step 6.2.1

Factor by grouping.

Tap for more steps...

Step 6.2.1.1

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 $a \cdot c = 9 \cdot - 8 = - 72$ and whose sum is $b = - 6$ .

Tap for more steps...

Step 6.2.1.1.1

Factor $- 6$ out of $- 6 c$ .

$- (9 c^{2} - 6 (c) - 8)$

Step 6.2.1.1.2

Rewrite $- 6$ as $6$ plus $- 12$

$- (9 c^{2} + (6 - 12) c - 8)$

Step 6.2.1.1.3

Apply the distributive property.

$- (9 c^{2} + 6 c - 12 c - 8)$

Step 6.2.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 6.2.1.2.1

Group the first two terms and the last two terms.

$- ((9 c^{2} + 6 c) - 12 c - 8)$

Step 6.2.1.2.2

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

$- (3 c (3 c + 2) - 4 (3 c + 2))$

Step 6.2.1.3

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

$- ((3 c + 2) (3 c - 4))$

Step 6.2.2

Remove unnecessary parentheses.

$- (3 c + 2) (3 c - 4)$