Solve by Factoring 7x^2-19x-6=0

$7 x^{2} - 19 x - 6 = 0$

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 $a \cdot c = 7 \cdot - 6 = - 42$ and whose sum is $b = - 19$ .

Factor $- 19$ out of $- 19 x$ .

$7 x^{2} - 19 x - 6 = 0$

Rewrite $- 19$ as $2$ plus $- 21$

$7 x^{2} + (2 - 21) x - 6 = 0$

Apply the distributive property.

$7 x^{2} + 2 x - 21 x - 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 2 x) - 21 x - 6 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $7 x + 2$ .

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

Step 2

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

$7 x + 2 = 0$

$x - 3 = 0$

Step 3

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

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

$7 x + 2 = 0$

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

Subtract $2$ from both sides of the equation.

$7 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 5

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

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

Solve by Factoring 7x^2-19x-6=0

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