Solve for x (x-2)(x-8)=-9

$(x - 2) (x - 8) = - 9$

Simplify $(x - 2) (x - 8)$ .

Expand $(x - 2) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$x (x - 8) - 2 (x - 8) = - 9$

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 2 (x - 8) = - 9$

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 2 x - 2 \cdot - 8 = - 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 8 - 2 x - 2 \cdot - 8 = - 9$

Move $- 8$ to the left of $x$ .

$x^{2} - 8 \cdot x - 2 x - 2 \cdot - 8 = - 9$

Multiply $- 2$ by $- 8$ .

$x^{2} - 8 x - 2 x + 16 = - 9$

Subtract $2 x$ from $- 8 x$ .

$x^{2} - 10 x + 16 = - 9$

Add $9$ to both sides of the equation.

$x^{2} - 10 x + 16 + 9 = 0$

Add $16$ and $9$ .

$x^{2} - 10 x + 25 = 0$

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$x^{2} - 10 x + 5^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 5 + 5^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 5$ .

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

Set the $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$