Solve for w 3w^2+14w+8=0

$3 w^{2} + 14 w + 8 = 0$

Step 1

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 $b = 14$ .

Factor $14$ out of $14 w$ .

$3 w^{2} + 14 (w) + 8 = 0$

Rewrite $14$ as $2$ plus $12$

$3 w^{2} + (2 + 12) w + 8 = 0$

Apply the distributive property.

$3 w^{2} + 2 w + 12 w + 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 w^{2} + 2 w) + 12 w + 8 = 0$

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

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

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

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

Step 2

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

$3 w + 2 = 0$

$w + 4 = 0$

Step 3

Set $3 w + 2$ equal to $0$ and solve for $w$ .

Set $3 w + 2$ equal to $0$ .

$3 w + 2 = 0$

Solve $3 w + 2 = 0$ for $w$ .

Subtract $2$ from both sides of the equation.

$3 w = - 2$

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

Divide each term in $3 w = - 2$ by $3$ .

$\frac{3 w}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 w}{3} = \frac{- 2}{3}$

Divide $w$ by $1$ .

$w = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{2}{3}$

Step 4

Set $w + 4$ equal to $0$ and solve for $w$ .

Set $w + 4$ equal to $0$ .

$w + 4 = 0$

Subtract $4$ from both sides of the equation.

$w = - 4$

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$w = - 0.\overline{6}, - 4$

Solve for w 3w^2+14w+8=0

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