Solve by Factoring -12x^2=34x-28

$- 12 x^{2} = 34 x - 28$

Step 1

Move all the expressions to the left side of the equation.

Subtract $34 x$ from both sides of the equation.

$- 12 x^{2} - 34 x = - 28$

Add $28$ to both sides of the equation.

$- 12 x^{2} - 34 x + 28 = 0$

Step 2

Factor $2$ out of $- 12 x^{2} - 34 x + 28$ .

Factor $2$ out of $- 12 x^{2}$ .

$2 (- 6 x^{2}) - 34 x + 28 = 0$

Factor $2$ out of $- 34 x$ .

$2 (- 6 x^{2}) + 2 (- 17 x) + 28 = 0$

Factor $2$ out of $28$ .

$2 (- 6 x^{2}) + 2 (- 17 x) + 2 (14) = 0$

Factor $2$ out of $2 (- 6 x^{2}) + 2 (- 17 x)$ .

$2 (- 6 x^{2} - 17 x) + 2 (14) = 0$

Factor $2$ out of $2 (- 6 x^{2} - 17 x) + 2 (14)$ .

$2 (- 6 x^{2} - 17 x + 14) = 0$

Step 3

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 $a \cdot c = - 6 \cdot 14 = - 84$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$2 (- 6 x^{2} - 17 x + 14) = 0$

Rewrite $- 17$ as $4$ plus $- 21$

$2 (- 6 x^{2} + (4 - 21) x + 14) = 0$

Apply the distributive property.

$2 (- 6 x^{2} + 4 x - 21 x + 14) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((- 6 x^{2} + 4 x) - 21 x + 14) = 0$

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

$2 (2 x (- 3 x + 2) + 7 (- 3 x + 2)) = 0$

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

$2 ((- 3 x + 2) (2 x + 7)) = 0$

Remove unnecessary parentheses.

$2 (- 3 x + 2) (2 x + 7) = 0$

Step 4

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

$- 3 x + 2 = 0$

$2 x + 7 = 0$

Step 5

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

Set $- 3 x + 2$ equal to $0$ .

$- 3 x + 2 = 0$

Solve $- 3 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- 3 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

Step 6

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 7

The final solution is all the values that make $2 (- 3 x + 2) (2 x + 7) = 0$ true.

$x = \frac{2}{3}, - \frac{7}{2}$

Solve by Factoring -12x^2=34x-28

Related Questions

Support LCMGCF.com by disabling your adblocker.