Solve for x (2x+1)(x-1)=-16x-8

$(2 x + 1) (x - 1) = - 16 x - 8$

Step 1

Simplify $(2 x + 1) (x - 1)$ .

Rewrite.

$0 + 0 + (2 x + 1) (x - 1) = - 16 x - 8$

Simplify by adding zeros.

$(2 x + 1) (x - 1) = - 16 x - 8$

Expand $(2 x + 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (x - 1) + 1 (x - 1) = - 16 x - 8$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 1 (x - 1) = - 16 x - 8$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 1 x + 1 \cdot - 1 = - 16 x - 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 1 + 1 x + 1 \cdot - 1 = - 16 x - 8$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 1 + 1 x + 1 \cdot - 1 = - 16 x - 8$

Multiply $- 1$ by $2$ .

$2 x^{2} - 2 x + 1 x + 1 \cdot - 1 = - 16 x - 8$

Multiply $x$ by $1$ .

$2 x^{2} - 2 x + x + 1 \cdot - 1 = - 16 x - 8$

Multiply $- 1$ by $1$ .

$2 x^{2} - 2 x + x - 1 = - 16 x - 8$

Add $- 2 x$ and $x$ .

$2 x^{2} - x - 1 = - 16 x - 8$

Step 2

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

Add $16 x$ to both sides of the equation.

$2 x^{2} - x - 1 + 16 x = - 8$

Add $- x$ and $16 x$ .

$2 x^{2} + 15 x - 1 = - 8$

Step 3

Add $8$ to both sides of the equation.

$2 x^{2} + 15 x - 1 + 8 = 0$

Step 4

Add $- 1$ and $8$ .

$2 x^{2} + 15 x + 7 = 0$

Step 5

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 $a \cdot c = 2 \cdot 7 = 14$ and whose sum is $b = 15$ .

Factor $15$ out of $15 x$ .

$2 x^{2} + 15 (x) + 7 = 0$

Rewrite $15$ as $1$ plus $14$

$2 x^{2} + (1 + 14) x + 7 = 0$

Apply the distributive property.

$2 x^{2} + 1 x + 14 x + 7 = 0$

Multiply $x$ by $1$ .

$2 x^{2} + x + 14 x + 7 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + x) + 14 x + 7 = 0$

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

$x (2 x + 1) + 7 (2 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (x + 7) = 0$

Step 6

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

$2 x + 1 = 0$

$x + 7 = 0$

Step 7

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 8

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 9

The final solution is all the values that make $(2 x + 1) (x + 7) = 0$ true.

$x = - \frac{1}{2}, - 7$

Step 10

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, - 7$

Decimal Form:

$x = - 0.5, - 7$

Solve for x (2x+1)(x-1)=-16x-8

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