Solve by Factoring 15x^2-x-6=0

$15 x^{2} - x - 6 = 0$

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 $a \cdot c = 15 \cdot - 6 = - 90$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$15 x^{2} - (x) - 6 = 0$

Rewrite $- 1$ as $9$ plus $- 10$

$15 x^{2} + (9 - 10) x - 6 = 0$

Apply the distributive property.

$15 x^{2} + 9 x - 10 x - 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 9 x) - 10 x - 6 = 0$

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

$3 x (5 x + 3) - 2 (5 x + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 3$ .

$(5 x + 3) (3 x - 2) = 0$

Step 2

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

$5 x + 3 = 0$

$3 x - 2 = 0$

Step 3

Set $5 x + 3$ equal to $0$ and solve for $x$ .

Set $5 x + 3$ equal to $0$ .

$5 x + 3 = 0$

Solve $5 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

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 $x$ .

Add $2$ to 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 $1$ .

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

Step 5

The final solution is all the values that make $(5 x + 3) (3 x - 2) = 0$ true.

$x = - \frac{3}{5}, \frac{2}{3}$

Solve by Factoring 15x^2-x-6=0

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