Solve by Factoring 6x^2+2x-8=0

$6 x^{2} + 2 x - 8 = 0$

Step 1

Factor $2$ out of $6 x^{2} + 2 x - 8$ .

Factor $2$ out of $6 x^{2}$ .

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 8$ .

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

Factor $2$ out of $2 (3 x^{2}) + 2 x$ .

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

Factor $2$ out of $2 (3 x^{2} + x) + 2 \cdot - 4$ .

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

Step 2

Factor.

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 $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

$2 (3 x^{2} + 1 x - 4) = 0$

Rewrite $1$ as $- 3$ plus $4$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 (3 x (x - 1) + 4 (x - 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$2 ((x - 1) (3 x + 4)) = 0$

Remove unnecessary parentheses.

$2 (x - 1) (3 x + 4) = 0$

Step 3

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

$x - 1 = 0$

$3 x + 4 = 0$

Step 4

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 5

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

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

$3 x + 4 = 0$

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

Subtract $4$ from both sides of the equation.

$3 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

The final solution is all the values that make $2 (x - 1) (3 x + 4) = 0$ true.

$x = 1, - \frac{4}{3}$

Solve by Factoring 6x^2+2x-8=0

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