(x-5)(x-6)=0

Solution for (x-5)(x-6)=0 equation:

Simplifying
(x + -5)(x + -6) = 0

Reorder the terms:
(-5 + x)(x + -6) = 0

Reorder the terms:
(-5 + x)(-6 + x) = 0

Multiply (-5 + x) * (-6 + x)
(-5(-6 + x) + x(-6 + x)) = 0
((-6 * -5 + x * -5) + x(-6 + x)) = 0
((30 + -5x) + x(-6 + x)) = 0
(30 + -5x + (-6 * x + x * x)) = 0
(30 + -5x + (-6x + x2)) = 0

Combine like terms: -5x + -6x = -11x
(30 + -11x + x2) = 0

Solving
30 + -11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {5, 6}