Solve for x (x+3)(x+1)=4x+7

$(x + 3) (x + 1) = 4 x + 7$

Step 1

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

Rewrite.

$0 + 0 + (x + 3) (x + 1) = 4 x + 7$

Simplify by adding zeros.

$(x + 3) (x + 1) = 4 x + 7$

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

Apply the distributive property.

$x (x + 1) + 3 (x + 1) = 4 x + 7$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 3 (x + 1) = 4 x + 7$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 3 x + 3 \cdot 1 = 4 x + 7$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 + 3 x + 3 \cdot 1 = 4 x + 7$

Multiply $x$ by $1$ .

$x^{2} + x + 3 x + 3 \cdot 1 = 4 x + 7$

Multiply $3$ by $1$ .

$x^{2} + x + 3 x + 3 = 4 x + 7$

Add $x$ and $3 x$ .

$x^{2} + 4 x + 3 = 4 x + 7$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$x^{2} + 4 x + 3 - 4 x = 7$

Combine the opposite terms in $x^{2} + 4 x + 3 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$x^{2} + 0 + 3 = 7$

Add $x^{2}$ and $0$ .

$x^{2} + 3 = 7$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x^{2} = 7 - 3$

Subtract $3$ from $7$ .

$x^{2} = 4$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{4}$

Step 5

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$

Solve for x (x+3)(x+1)=4x+7

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