Solve by Factoring 3x^2-14x-5=0

$3 x^{2} - 14 x - 5 = 0$

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 $a \cdot c = 3 \cdot - 5 = - 15$ and whose sum is $b = - 14$ .

Factor $- 14$ out of $- 14 x$ .

$3 x^{2} - 14 x - 5 = 0$

Rewrite $- 14$ as $1$ plus $- 15$

$3 x^{2} + (1 - 15) x - 5 = 0$

Apply the distributive property.

$3 x^{2} + 1 x - 15 x - 5 = 0$

Multiply $x$ by $1$ .

$3 x^{2} + x - 15 x - 5 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + x) - 15 x - 5 = 0$

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

$x (3 x + 1) - 5 (3 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$(3 x + 1) (x - 5) = 0$

Step 2

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

$3 x + 1 = 0$

$x - 5 = 0$

Step 3

Set $3 x + 1$ equal to $0$ and solve for $x$ .

Set $3 x + 1$ equal to $0$ .

$3 x + 1 = 0$

Solve $3 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 5

The final solution is all the values that make $(3 x + 1) (x - 5) = 0$ true.

$x = - \frac{1}{3}, 5$

Solve by Factoring 3x^2-14x-5=0

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