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

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

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

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

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

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

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

Solving
30 + -11x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
30 + -6 + -11x + x2 = 6 + -6

Combine like terms: 30 + -6 = 24
24 + -11x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
24 + -11x + x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {3, 8}