(x-2)(12-x)=9

Solution for (x-2)(12-x)=9 equation:

Simplifying
(x + -2)(12 + -1x) = 9

Reorder the terms:
(-2 + x)(12 + -1x) = 9

Multiply (-2 + x) * (12 + -1x)
(-2(12 + -1x) + x(12 + -1x)) = 9
((12 * -2 + -1x * -2) + x(12 + -1x)) = 9
((-24 + 2x) + x(12 + -1x)) = 9
(-24 + 2x + (12 * x + -1x * x)) = 9
(-24 + 2x + (12x + -1x2)) = 9

Combine like terms: 2x + 12x = 14x
(-24 + 14x + -1x2) = 9

Solving
-24 + 14x + -1x2 = 9

Solving for variable 'x'.

Reorder the terms:
-24 + -9 + 14x + -1x2 = 9 + -9

Combine like terms: -24 + -9 = -33
-33 + 14x + -1x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-33 + 14x + -1x2 = 0

Factor a trinomial.
(-11 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Simplifying
x = 11
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {11, 3}