Solve for x 12x^2+23x-24=0

$12 x^{2} + 23 x - 24 = 0$

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 $a \cdot c = 12 \cdot - 24 = - 288$ and whose sum is $b = 23$ .

Factor $23$ out of $23 x$ .

$12 x^{2} + 23 (x) - 24 = 0$

Rewrite $23$ as $- 9$ plus $32$

$12 x^{2} + (- 9 + 32) x - 24 = 0$

Apply the distributive property.

$12 x^{2} - 9 x + 32 x - 24 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} - 9 x) + 32 x - 24 = 0$

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

$3 x (4 x - 3) + 8 (4 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x - 3$ .

$(4 x - 3) (3 x + 8) = 0$

Step 2

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

$4 x - 3 = 0$

$3 x + 8 = 0$

Step 3

Set $4 x - 3$ equal to $0$ and solve for $x$ .

Set $4 x - 3$ equal to $0$ .

$4 x - 3 = 0$

Solve $4 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$4 x = 3$

Divide each term in $4 x = 3$ by $4$ and simplify.

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

Step 4

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

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

$3 x + 8 = 0$

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

Subtract $8$ from both sides of the equation.

$3 x = - 8$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The final solution is all the values that make $(4 x - 3) (3 x + 8) = 0$ true.

$x = \frac{3}{4}, - \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}, - \frac{8}{3}$

Decimal Form:

$x = 0.75, - 2.\overline{6}$

Mixed Number Form:

$x = \frac{3}{4}, - 2 \frac{2}{3}$

Solve for x 12x^2+23x-24=0

Related Questions

Support LCMGCF.com by disabling your adblocker.