Solve for x (2x-1)(x+3)=4

$(2 x - 1) (x + 3) = 4$

Step 1

Simplify $(2 x - 1) (x + 3)$ .

Expand $(2 x - 1) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$2 x (x + 3) - 1 (x + 3) = 4$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 3 - 1 (x + 3) = 4$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 3 - 1 x - 1 \cdot 3 = 4$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 3 - 1 x - 1 \cdot 3 = 4$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 3 - 1 x - 1 \cdot 3 = 4$

Multiply $3$ by $2$ .

$2 x^{2} + 6 x - 1 x - 1 \cdot 3 = 4$

Rewrite $- 1 x$ as $- x$ .

$2 x^{2} + 6 x - x - 1 \cdot 3 = 4$

Multiply $- 1$ by $3$ .

$2 x^{2} + 6 x - x - 3 = 4$

Subtract $x$ from $6 x$ .

$2 x^{2} + 5 x - 3 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$2 x^{2} + 5 x - 3 - 4 = 0$

Step 3

Subtract $4$ from $- 3$ .

$2 x^{2} + 5 x - 7 = 0$

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 $a \cdot c = 2 \cdot - 7 = - 14$ and whose sum is $b = 5$ .

Factor $5$ out of $5 x$ .

$2 x^{2} + 5 (x) - 7 = 0$

Rewrite $5$ as $- 2$ plus $7$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 5

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

$x - 1 = 0$

$2 x + 7 = 0$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 8

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

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1, - 3.5$

Mixed Number Form:

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

Solve for x (2x-1)(x+3)=4

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