Solve by Factoring -8x^3-13x^2+6x=0

$- 8 x^{3} - 13 x^{2} + 6 x = 0$

Step 1

Factor $x$ out of $- 8 x^{3} - 13 x^{2} + 6 x$ .

Factor $x$ out of $- 8 x^{3}$ .

$x (- 8 x^{2}) - 13 x^{2} + 6 x = 0$

Factor $x$ out of $- 13 x^{2}$ .

$x (- 8 x^{2}) + x (- 13 x) + 6 x = 0$

Factor $x$ out of $6 x$ .

$x (- 8 x^{2}) + x (- 13 x) + x \cdot 6 = 0$

Factor $x$ out of $x (- 8 x^{2}) + x (- 13 x)$ .

$x (- 8 x^{2} - 13 x) + x \cdot 6 = 0$

Factor $x$ out of $x (- 8 x^{2} - 13 x) + x \cdot 6$ .

$x (- 8 x^{2} - 13 x + 6) = 0$

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 $a \cdot c = - 8 \cdot 6 = - 48$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$x (- 8 x^{2} - 13 x + 6) = 0$

Rewrite $- 13$ as $3$ plus $- 16$

$x (- 8 x^{2} + (3 - 16) x + 6) = 0$

Apply the distributive property.

$x (- 8 x^{2} + 3 x - 16 x + 6) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$x ((- 8 x^{2} + 3 x) - 16 x + 6) = 0$

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

$x (x (- 8 x + 3) + 2 (- 8 x + 3)) = 0$

Factor the polynomial by factoring out the greatest common factor, $- 8 x + 3$ .

$x ((- 8 x + 3) (x + 2)) = 0$

Remove unnecessary parentheses.

$x (- 8 x + 3) (x + 2) = 0$

Step 3

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

$x = 0$

$- 8 x + 3 = 0$

$x + 2 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $- 8 x + 3$ equal to $0$ and solve for $x$ .

Set $- 8 x + 3$ equal to $0$ .

$- 8 x + 3 = 0$

Solve $- 8 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$- 8 x = - 3$

Divide each term in $- 8 x = - 3$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 3$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 3}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 3}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 8}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{3}{8}$

Step 6

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $x (- 8 x + 3) (x + 2) = 0$ true.

$x = 0, \frac{3}{8}, - 2$

Solve by Factoring -8x^3-13x^2+6x=0

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