Solve for x 2x^2-8x-10=x+8

$2 x^{2} - 8 x - 10 = x + 8$

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

Subtract $x$ from both sides of the equation.

$2 x^{2} - 8 x - 10 - x = 8$

Subtract $x$ from $- 8 x$ .

$2 x^{2} - 9 x - 10 = 8$

Subtract $8$ from both sides of the equation.

$2 x^{2} - 9 x - 10 - 8 = 0$

Subtract $8$ from $- 10$ .

$2 x^{2} - 9 x - 18 = 0$

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 $a \cdot c = 2 \cdot - 18 = - 36$ and whose sum is $b = - 9$ .

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

$2 x^{2} - 9 x - 18 = 0$

Rewrite $- 9$ as $3$ plus $- 12$

$2 x^{2} + (3 - 12) x - 18 = 0$

Apply the distributive property.

$2 x^{2} + 3 x - 12 x - 18 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 3 x) - 12 x - 18 = 0$

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

$x (2 x + 3) - 6 (2 x + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 3$ .

$(2 x + 3) (x - 6) = 0$

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

$2 x + 3 = 0$

$x - 6 = 0$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

The final solution is all the values that make $(2 x + 3) (x - 6) = 0$ true.

$x = - \frac{3}{2}, 6$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{2}, 6$

Decimal Form:

$x = - 1.5, 6$

Mixed Number Form:

$x = - 1 \frac{1}{2}, 6$

Solve for x 2x^2-8x-10=x+8

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