(x-9)(2-x)=0

Solution for (x-9)(2-x)=0 equation:

Simplifying
(x + -9)(2 + -1x) = 0

Reorder the terms:
(-9 + x)(2 + -1x) = 0

Multiply (-9 + x) * (2 + -1x)
(-9(2 + -1x) + x(2 + -1x)) = 0
((2 * -9 + -1x * -9) + x(2 + -1x)) = 0
((-18 + 9x) + x(2 + -1x)) = 0
(-18 + 9x + (2 * x + -1x * x)) = 0
(-18 + 9x + (2x + -1x2)) = 0

Combine like terms: 9x + 2x = 11x
(-18 + 11x + -1x2) = 0

Solving
-18 + 11x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {9, 2}