Solve for x 12x^2-26x-7=3x+1

$12 x^{2} - 26 x - 7 = 3 x + 1$

Step 1

Move all terms containing $x$ to the left side of the equation.

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

$12 x^{2} - 26 x - 7 - 3 x = 1$

Subtract $3 x$ from $- 26 x$ .

$12 x^{2} - 29 x - 7 = 1$

Step 2

Subtract $1$ from both sides of the equation.

$12 x^{2} - 29 x - 7 - 1 = 0$

Step 3

Subtract $1$ from $- 7$ .

$12 x^{2} - 29 x - 8 = 0$

Step 4

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 $a \cdot c = 12 \cdot - 8 = - 96$ and whose sum is $b = - 29$ .

Factor $- 29$ out of $- 29 x$ .

$12 x^{2} - 29 x - 8 = 0$

Rewrite $- 29$ as $3$ plus $- 32$

$12 x^{2} + (3 - 32) x - 8 = 0$

Apply the distributive property.

$12 x^{2} + 3 x - 32 x - 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 3 x) - 32 x - 8 = 0$

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

$3 x (4 x + 1) - 8 (4 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (3 x - 8) = 0$

Step 5

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

$4 x + 1 = 0$

$3 x - 8 = 0$

Step 6

Set $4 x + 1$ equal to $0$ and solve for $x$ .

Set $4 x + 1$ equal to $0$ .

$4 x + 1 = 0$

Solve $4 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$4 x = - 1$

Divide each term in $4 x = - 1$ by $4$ and simplify.

Divide each term in $4 x = - 1$ by $4$ .

$\frac{4 x}{4} = \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 1}{4}$

Divide $x$ by $1$ .

$x = \frac{- 1}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

Step 7

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 $x$ .

Add $8$ to 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 $1$ .

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

Step 8

The final solution is all the values that make $(4 x + 1) (3 x - 8) = 0$ true.

$x = - \frac{1}{4}, \frac{8}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{4}, \frac{8}{3}$

Decimal Form:

$x = - 0.25, 2.\overline{6}$

Mixed Number Form:

$x = - \frac{1}{4}, 2 \frac{2}{3}$

Solve for x 12x^2-26x-7=3x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.