Solve for c 3c^2+4c+8=-6c

$3 c^{2} + 4 c + 8 = - 6 c$

Step 1

Move all terms containing $c$ to the left side of the equation.

Add $6 c$ to both sides of the equation.

$3 c^{2} + 4 c + 8 + 6 c = 0$

Add $4 c$ and $6 c$ .

$3 c^{2} + 10 c + 8 = 0$

Step 2

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = 10$ .

Factor $10$ out of $10 c$ .

$3 c^{2} + 10 (c) + 8 = 0$

Rewrite $10$ as $4$ plus $6$

$3 c^{2} + (4 + 6) c + 8 = 0$

Apply the distributive property.

$3 c^{2} + 4 c + 6 c + 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 c^{2} + 4 c) + 6 c + 8 = 0$

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

$c (3 c + 4) + 2 (3 c + 4) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 c + 4$ .

$(3 c + 4) (c + 2) = 0$

Step 3

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

$3 c + 4 = 0$

$c + 2 = 0$

Step 4

Set $3 c + 4$ equal to $0$ and solve for $c$ .

Set $3 c + 4$ equal to $0$ .

$3 c + 4 = 0$

Solve $3 c + 4 = 0$ for $c$ .

Subtract $4$ from both sides of the equation.

$3 c = - 4$

Divide each term in $3 c = - 4$ by $3$ and simplify.

Divide each term in $3 c = - 4$ by $3$ .

$\frac{3 c}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 c}{3} = \frac{- 4}{3}$

Divide $c$ by $1$ .

$c = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$c = - \frac{4}{3}$

Step 5

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

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

$c + 2 = 0$

Subtract $2$ from both sides of the equation.

$c = - 2$

Step 6

The final solution is all the values that make $(3 c + 4) (c + 2) = 0$ true.

$c = - \frac{4}{3}, - 2$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{4}{3}, - 2$

Decimal Form:

$c = - 1.\overline{3}, - 2$

Mixed Number Form:

$c = - 1 \frac{1}{3}, - 2$

Solve for c 3c^2+4c+8=-6c

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