Basic Math Examples

$- 3 c^{2} - 4 c + 4 = 0$

Step 1

Factor the left side of the equation.

Tap for more steps...

Step 1.1

Factor $- 1$ out of $- 3 c^{2} - 4 c + 4$ .

Tap for more steps...

Step 1.1.1

Factor $- 1$ out of $- 3 c^{2}$ .

$- (3 c^{2}) - 4 c + 4 = 0$

Step 1.1.2

Factor $- 1$ out of $- 4 c$ .

$- (3 c^{2}) - (4 c) + 4 = 0$

Step 1.1.3

Rewrite $4$ as $- 1 (- 4)$ .

$- (3 c^{2}) - (4 c) - 1 \cdot - 4 = 0$

Step 1.1.4

Factor $- 1$ out of $- (3 c^{2}) - (4 c)$ .

$- (3 c^{2} + 4 c) - 1 \cdot - 4 = 0$

Step 1.1.5

Factor $- 1$ out of $- (3 c^{2} + 4 c) - 1 (- 4)$ .

$- (3 c^{2} + 4 c - 4) = 0$

Step 1.2

Factor.

Tap for more steps...

Step 1.2.1

Factor by grouping.

Tap for more steps...

Step 1.2.1.1

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 $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = 4$ .

Tap for more steps...

Step 1.2.1.1.1

Factor $4$ out of $4 c$ .

$- (3 c^{2} + 4 (c) - 4) = 0$

Step 1.2.1.1.2

Rewrite $4$ as $- 2$ plus $6$

$- (3 c^{2} + (- 2 + 6) c - 4) = 0$

Step 1.2.1.1.3

Apply the distributive property.

$- (3 c^{2} - 2 c + 6 c - 4) = 0$

Step 1.2.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.2.1.2.1

Group the first two terms and the last two terms.

$- ((3 c^{2} - 2 c) + 6 c - 4) = 0$

Step 1.2.1.2.2

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

$- (c (3 c - 2) + 2 (3 c - 2)) = 0$

Step 1.2.1.3

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

$- ((3 c - 2) (c + 2)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$- (3 c - 2) (c + 2) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$3 c - 2 = 0$

$c + 2 = 0$

Step 3

Set $3 c - 2$ equal to $0$ and solve for $c$ .

Tap for more steps...

Step 3.1

Set $3 c - 2$ equal to $0$ .

$3 c - 2 = 0$

Step 3.2

Solve $3 c - 2 = 0$ for $c$ .

Tap for more steps...

Step 3.2.1

Add $2$ to both sides of the equation.

$3 c = 2$

Step 3.2.2

Divide each term in $3 c = 2$ by $3$ and simplify.

Tap for more steps...

Step 3.2.2.1

Divide each term in $3 c = 2$ by $3$ .

$\frac{3 c}{3} = \frac{2}{3}$

Step 3.2.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{3 c}{3} = \frac{2}{3}$

Step 3.2.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{2}{3}$

Step 4

Set $c + 2$ equal to $0$ and solve for $c$ .

Tap for more steps...

Step 4.1

Set $c + 2$ equal to $0$ .

$c + 2 = 0$

Step 4.2

Subtract $2$ from both sides of the equation.

$c = - 2$

Step 5

The final solution is all the values that make $- (3 c - 2) (c + 2) = 0$ true.

$c = \frac{2}{3}, - 2$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \frac{2}{3}, - 2$

Decimal Form:

$c = 0.\overline{6}, - 2$