(x-11)(x-5)=0

Solution for (x-11)(x-5)=0 equation:

Simplifying
(x + -11)(x + -5) = 0

Reorder the terms:
(-11 + x)(x + -5) = 0

Reorder the terms:
(-11 + x)(-5 + x) = 0

Multiply (-11 + x) * (-5 + x)
(-11(-5 + x) + x(-5 + x)) = 0
((-5 * -11 + x * -11) + x(-5 + x)) = 0
((55 + -11x) + x(-5 + x)) = 0
(55 + -11x + (-5 * x + x * x)) = 0
(55 + -11x + (-5x + x2)) = 0

Combine like terms: -11x + -5x = -16x
(55 + -16x + x2) = 0

Solving
55 + -16x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

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

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {5, 11}