Solve for k 3k^2-14k+4=-4

$3 k^{2} - 14 k + 4 = - 4$

Add $4$ to both sides of the equation.

$3 k^{2} - 14 k + 4 + 4 = 0$

Add $4$ and $4$ .

$3 k^{2} - 14 k + 8 = 0$

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 $- 14 k$ .

$3 k^{2} - 14 k + 8 = 0$

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

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

Apply the distributive property.

$3 k^{2} - 2 k - 12 k + 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$k (3 k - 2) - 4 (3 k - 2) = 0$

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

$(3 k - 2) (k - 4) = 0$

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

$3 k - 2 = 0$

$k - 4 = 0$

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

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

$3 k - 2 = 0$

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

Add $2$ to both sides of the equation.

$3 k = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Set $k - 4$ equal to $0$ and solve for $k$ .

Set $k - 4$ equal to $0$ .

$k - 4 = 0$

Add $4$ to both sides of the equation.

$k = 4$

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

$k = \frac{2}{3}, 4$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{2}{3}, 4$

Decimal Form:

$k = 0.\overline{6}, 4$

Solve for k 3k^2-14k+4=-4

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