Solve by Factoring 12x^2-9x-3x^3=0

$12 x^{2} - 9 x - 3 x^{3} = 0$

Factor $3 x$ out of $12 x^{2} - 9 x - 3 x^{3}$ .

Factor $3 x$ out of $12 x^{2}$ .

$3 x (4 x) - 9 x - 3 x^{3} = 0$

Factor $3 x$ out of $- 9 x$ .

$3 x (4 x) + 3 x (- 3) - 3 x^{3} = 0$

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

$3 x (4 x) + 3 x (- 3) + 3 x (- x^{2}) = 0$

Factor $3 x$ out of $3 x (4 x) + 3 x (- 3)$ .

$3 x (4 x - 3) + 3 x (- x^{2}) = 0$

Factor $3 x$ out of $3 x (4 x - 3) + 3 x (- x^{2})$ .

$3 x (4 x - 3 - x^{2}) = 0$

Factor.

Factor by grouping.

Reorder terms.

$3 x (- x^{2} + 4 x - 3) = 0$

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 $a \cdot c = - 1 \cdot - 3 = 3$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

$3 x (- x^{2} + 4 (x) - 3) = 0$

Rewrite $4$ as $1$ plus $3$

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Remove unnecessary parentheses.

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

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

$x = 0$

$- x + 1 = 0$

$x - 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$- x + 1 = 0$

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

Subtract $1$ from both sides of the equation.

$- x = - 1$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$

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.

$x = 3$

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

$x = 0, 1, 3$

Solve by Factoring 12x^2-9x-3x^3=0

Related Questions

Support LCMGCF.com by disabling your adblocker.