Solve for x x(x-2)+x-2=0

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

Step 1

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

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot - 2 + x - 2 = 0$

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 + x - 2 = 0$

Move $- 2$ to the left of $x$ .

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

Add $- 2 x$ and $x$ .

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

Step 2

Factor $x^{2} - x - 2$ 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 $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

Step 3

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 4

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 5

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 6

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

$x = 2, - 1$

Solve for x x(x-2)+x-2=0

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