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

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

Step 1

Simplify $2 (x - 4) - (x + 2)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

$2 x - 8 - (x + 2) = (x + 2) (x - 4)$

Apply the distributive property.

$2 x - 8 - x - 1 \cdot 2 = (x + 2) (x - 4)$

Multiply $- 1$ by $2$ .

$2 x - 8 - x - 2 = (x + 2) (x - 4)$

Simplify by adding terms.

Subtract $x$ from $2 x$ .

$x - 8 - 2 = (x + 2) (x - 4)$

Subtract $2$ from $- 8$ .

$x - 10 = (x + 2) (x - 4)$

Step 2

Simplify $(x + 2) (x - 4)$ .

Expand $(x + 2) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x - 10 = x (x - 4) + 2 (x - 4)$

Apply the distributive property.

$x - 10 = x \cdot x + x \cdot - 4 + 2 (x - 4)$

Apply the distributive property.

$x - 10 = x \cdot x + x \cdot - 4 + 2 x + 2 \cdot - 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x - 10 = x^{2} + x \cdot - 4 + 2 x + 2 \cdot - 4$

Move $- 4$ to the left of $x$ .

$x - 10 = x^{2} - 4 \cdot x + 2 x + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$x - 10 = x^{2} - 4 x + 2 x - 8$

Add $- 4 x$ and $2 x$ .

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

Step 3

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 4

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

Subtract $x$ from both sides of the equation.

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

Subtract $x$ from $- 2 x$ .

$x^{2} - 3 x - 8 = - 10$

Step 5

Add $10$ to both sides of the equation.

$x^{2} - 3 x - 8 + 10 = 0$

Step 6

Add $- 8$ and $10$ .

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

Step 7

Factor $x^{2} - 3 x + 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $- 3$ .

$- 2, - 1$

Write the factored form using these integers.

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

Step 8

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

$x - 2 = 0$

$x - 1 = 0$

Step 9

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 10

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 11

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

$x = 2, 1$

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

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