Solve by Factoring 24x^2-11x-3=3x

$24 x^{2} - 11 x - 3 = 3 x$

Step 1

Subtract $3 x$ from both sides of the equation.

$24 x^{2} - 11 x - 3 - 3 x = 0$

Step 2

Subtract $3 x$ from $- 11 x$ .

$24 x^{2} - 14 x - 3 = 0$

Step 3

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 $a \cdot c = 24 \cdot - 3 = - 72$ and whose sum is $b = - 14$ .

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

$24 x^{2} - 14 x - 3 = 0$

Rewrite $- 14$ as $4$ plus $- 18$

$24 x^{2} + (4 - 18) x - 3 = 0$

Apply the distributive property.

$24 x^{2} + 4 x - 18 x - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(24 x^{2} + 4 x) - 18 x - 3 = 0$

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

$4 x (6 x + 1) - 3 (6 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $6 x + 1$ .

$(6 x + 1) (4 x - 3) = 0$

Step 4

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

$6 x + 1 = 0$

$4 x - 3 = 0$

Step 5

Set $6 x + 1$ equal to $0$ and solve for $x$ .

Set $6 x + 1$ equal to $0$ .

$6 x + 1 = 0$

Solve $6 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$6 x = - 1$

Divide each term in $6 x = - 1$ by $6$ and simplify.

Divide each term in $6 x = - 1$ by $6$ .

$\frac{6 x}{6} = \frac{- 1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 1}{6}$

Divide $x$ by $1$ .

$x = \frac{- 1}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{6}$

Step 6

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 7

The final solution is all the values that make $(6 x + 1) (4 x - 3) = 0$ true.

$x = - \frac{1}{6}, \frac{3}{4}$

Solve by Factoring 24x^2-11x-3=3x

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