(x-11)(-x+9)=0

Solution for (x-11)(-x+9)=0 equation:

Simplifying
(x + -11)(-1x + 9) = 0

Reorder the terms:
(-11 + x)(-1x + 9) = 0

Reorder the terms:
(-11 + x)(9 + -1x) = 0

Multiply (-11 + x) * (9 + -1x)
(-11(9 + -1x) + x(9 + -1x)) = 0
((9 * -11 + -1x * -11) + x(9 + -1x)) = 0
((-99 + 11x) + x(9 + -1x)) = 0
(-99 + 11x + (9 * x + -1x * x)) = 0
(-99 + 11x + (9x + -1x2)) = 0

Combine like terms: 11x + 9x = 20x
(-99 + 20x + -1x2) = 0

Solving
-99 + 20x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-11 + x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {11, 9}